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Gesztesy, Fritz (ed.); Laptev, Ari (ed.); Pushnitski, Alexander (ed.); Shargorodsky, Eugene (ed.); Simon, Barry (ed.)

Editors’ introduction. (English) Zbl 07902918

J. Spectr. Theory 14, No. 2, 397-426 (2024).

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[1] Curriculum Vitae E. B. Davies Biographical data Full Name: Edward Brian DAVIES Date of Birth: 13th June 1944 Nationality: British. Born in Cardiff, Wales.
[2] B. A. Mathematics, University of Oxford, First Class. Junior Mathematical Prize, with special commendation.
[3] M. A. and D. Phil. Mathematics (Functional Analysis), University of Oxford. Senior Mathematical Prize. 1967-68 Junior Lecturer, Oxford University. 1968-69 Visiting Member, Institute for Advanced Study, Princeton. 1969-70 C.L.E. Moore Instructor, MIT, Cambridge, Mass. 1970-81 Tutorial Fellow, St. John’s College, Oxford. 1971-73 C.U.F. Lecturer, Mathematics Department, Oxford University. Autumn 1972 Visiting Member, Rockefeller University. 1973-1981 University Lecturer, Oxford University. April 1974 Visiting member, IHES, Bures-sur-Yvette, France. Spring 1975 Visiting member, Geneva University. 1973-1981 Joint Chief Editor, Quarterly Journal of Mathematics. 1974-1978 Member of Mathematics Faculty Board. 1974-1978 Chairman of the M.Sc. Examiners. Autumn 1977 Visiting Lecturer, Princeton University. 1973-1978 Organiser of quantum theory seminar. 1979-1981 Senior Dean, St. John’s College, Oxford.
[4] Spring 1980 Visiting Professor, Ecole Polytechnique Federale, Lausanne. From October 1981 Professor of Mathematics. King’s College London. 1983-1990 Founding Editor of London Mathematical Society Student Texts. 1984-1987 Member of SERC Mathematics Committee Research papers
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[6] The existence of characters on topological lattices. J. London Math. Soc. 43 (1968) 217-220. · Zbl 0164.33301
[7] The structure and ideal theory of the pre-dual of a Banach lattice Trans. Amer. Math. Soc. 131 (1968) 544-555. · Zbl 0159.41503
[8] On the Banach duals of certain spaces with the Riesz decomposition property. Quart. J. Math. Oxford (2) 18, (1967) 109-111. · Zbl 0147.11102
[9] Tensor products, infinite products and projective limits of Choquet simplexes. With G. Vincent Smith.Math. Scand. 22 (1968) 145-164. · Zbl 0176.42802
[10] The Choquet theory and representation of ordered Banach spaces. Illinois J. Math 13 (1969) 176-187. · Zbl 0165.46801
[11] On the Borel structure of C -algebras. Commun. Math. Phys. 8, 147-163 (1968). · Zbl 0153.44701
[12] The structure of Sigma*-algebras. Quart. J. Math. Oxford (2) 20 (1969) 351-366. · Zbl 0183.42201
[13] Decomposition of traces on separable C algebras. Quart. J. Math. Oxford (2), 20 (1969) 97-111. · Zbl 0172.17903
[14] An operational approach to quantum probability. With J. T. Lewis. Commun. Math. Phys. 17, 239-260 (1970). · Zbl 0194.58304
[15] On the repeated measurement of continuous observables in quantum mechan-ics. J. Functional Anal. 6 (1970) 318-346. · Zbl 0198.59901
[16] Quantum stochastic processes. Commun. Math. Phys. 15, 277-306 (1970). · Zbl 0184.54102
[17] Involutary automorphisms of operator algebras. Trans. Amer. Math. Soc. 158 (1971) 115-142. · Zbl 0219.46049
[18] Quantum stochastic processes II. Commun. Math. Phys. 19, 83-105 (1970). · Zbl 0199.28202
[19] A generalisation of Kaplansky’s theorem. J. London Math. Soc. 4 (1972) 435-436. · Zbl 0229.47015
[20] Quantum stochastic processes III. Commun. Math. Phys. 22, 51-70 (1971). · Zbl 0217.50701
[21] An example related to the foundations of quantum theory. J. Math. Phys. 13 (1972) 39-41. · Zbl 0229.02029
[22] Some contraction semigroups in quantum probability. Z. Wahrscheinlichkeits-theorie 23 (1972) 261-273. · Zbl 0231.20023
[23] Hilbert space representations of Lie algebras. Commun. Math. Phys. 23, 159-168 (1971). · Zbl 0222.46039
[24] Diffusion for weakly coupled quantum oscillators. Commun. Math. Phys. 27, 309-325 (1972).
[25] The thermodynamic limit for an imperfect Boson gas. Commun. Math, Phys. 28, 69-86 (1972).
[26] Properties of the Green’s functions of some Schrödinger operators. J. London Math. Soc. (2) 7 (1973) 483-491. · Zbl 0271.47003
[27] The ideal Boson gas in an external scalar potential. Commun. Math. Phys. 30, 229-247 (1972).
[28] The harmonic oscillator in a heat bath. Commun. Math, Phys. 33, 171-186 (1973).
[29] Exact dynamics of an infinite-atom Dicke maser model. Commun. Math. Phys. 33, 187-205 (1973).
[30] Dynamics of a multi-level Wigner-Weisskopf atom. J. Math. Phys. 15 (1974) 2036-2041.
[31] The infinite atom Dicke maser model II. Commun. Math. Phys. 34, 237-249 (1973).
[32] Symmetries of compact convex sets. Quart. J. Math., Oxford (2) 25 (1974) 323-328. · Zbl 0298.22018
[33] Parametric interactions and scattering. Commun. Math. Phys. 37 (1974) 161-174. · Zbl 0284.35061
[34] Time dependent scattering theory. Math. Ann. 210 (1974) 149-162. · Zbl 0287.47005
[35] Markovian master equations. Commun. Math. Phys. 39 (1974) 91-110. · Zbl 0294.60080
[36] Markovian master equations II. Math. Ann. 219 (1976) 147-158. · Zbl 0323.60061
[37] Markovian master equations III. Ann. Inst. H. Poincaré, sect. B, XI (1975) 265-273. · Zbl 0323.60062
[38] A model for absorption or decay. Helv. Phys. Acta 48 (1975) 365-382.
[39] The use of master equations in quantum mechanics. IASPS Conference Pro-ceedings. Warsaw 1975.
[40] Resonances, spectral concentration and exponential decay. Lett. Math. Phys. 1 (1975) 31-35. · Zbl 0346.47019
[41] Time decay for fermion systems with persistent vacuum, with J. P. Eckmann. Helv. Phys. Acta 48 (1975) 731-742.
[42] Asymptotic analysis of some abstract evolution equations. J. Functional Anal. 25 (1977) 81-101. · Zbl 0347.47021
[43] The classical limit for quantum dynamical semigroups. Commun. Math. Phys. 49 (1976) 113-129. · Zbl 0355.60069
[44] Eigenfunction expansions for singular Schrödinger operators. Arch. Rat. Mech. Anal. 63 (1977) 261-272. · Zbl 0352.35068
[45] Quantum dynamical semigroups and the neutron diffusion equation. Rep. Math. Phys. 11 (1977) 169-188. · Zbl 0372.47020
[46] First and second quantised neutron diffusion equations. Commun. Math. Phys. 52 (1977) 111-126.
[47] Quantum communication systems. I.E.E.E. Trans. Inf. Theory 23 (1977) 530-534. · Zbl 0359.94004
[48] Information and quantum measurements. I.E.E.E. Trans. Int. Theory 24 (1978) 596-599. · Zbl 0382.94009
[49] Dilations of completely positive maps. J. London Math. Soc. (2), 17 (1978) 330-338. · Zbl 0376.46037
[50] A model of atomic radiation. Ann. Inst. H. Poincare 28A (1978) 91-110. · Zbl 0386.46059
[51] Scattering from infinite sheets. Math. Proc. Camb. Phil. Soc. 82 (1977) 327-334. · Zbl 0362.47003
[52] Irreversible dynamics of infinite fermion systems. Commun. Math. Phys. 55 (1977) 231-258. · Zbl 0361.47013
[53] A model of heat conduction. J. Stat. Phys. 18 (1978) 161-170.
[54] Generators of dynamical semigroups. J. Functional Anal. 34 (1979) 421-432. · Zbl 0428.47021
[55] Master equations: a survey of rigourous results. Rend. Sem. Mat. Fis. Milano 47 (1977) 165-173. · Zbl 0407.60099
[56] Particle-boson interactions and the weak coupling limit. J. Math. Phys. 20 (1979) 345-351.
[57] With M. Aizenmann and E. H. Lieb: Positive linear maps which are order bounded on C -subalgebras. Adv. Math. 28 (1978) 84-86. · Zbl 0397.46058
[58] With H. Spohn: Open quantum systems with time-dependent Hamiltonians and their linear response. J. Stat. Phys. 19 (1978) 511-523.
[59] Uniqueness of the standard form of the generator of a quantum dynamical semi-group. Rep. Math. Phys. 17 (1980) 249-255. · Zbl 0493.47021
[60] Dynamical semigroups, generators and measurement theory. pp. 85-98 in “Mathematical Problems in the Quantum Theory of Irreversible Processes”, Proceedings of Arco Felice Symposium, April, 1978.
[61] With B. Simon: Scattering theory for systems with different spatial asymptotics on the left and right. Commun. Math. Phys. 63 (1978) 277-301. · Zbl 0393.34015
[62] Two-channel Hamiltonians and the optical model of nuclear scattering. Ann. Inst. H. Poincare 29A (1978) 395-413. · Zbl 0427.47004
[63] Symmetry breaking for a non-linear Schrödinger equation. Commun. Math. Phys. 64 (1979) 191-210. · Zbl 0405.35027
[64] Scattering from a spatially restricted atom I. Adv. Math. 34 (1979) 28-45. · Zbl 0414.47004
[65] Classical approximations to Gibbs states. Math. Proc. Camb. Phil. Soc. 86 (1979) 521-527. · Zbl 0456.46056
[66] Non-unitary scattering and capture I. Commun. Math. Phys. 71 (1980) 277-288. · Zbl 0428.47006
[67] Some time-dependent Hartree equations. Ann. Inst. H. Poincare 31A (1979) 319-337. · Zbl 0428.35023
[68] Irreversible and non-linear dynamics of open systems. Proc. NATO Advanced Study Institute, Cambridge 1979, ed. R. G. Woolley, Plenum Press, 1980.
[69] Asymptotic completeness for a quark model of meson scattering. Ann. Phys. 126 (1980) 171-185.
[70] On Enss’ approach to scattering theory. Duke Math. J. 47 (1980) 171-185. · Zbl 0434.47014
[71] Non-unitary scattering and capture II. Ann. Inst. H. Poincare 32A (1980) 361-375. · Zbl 0445.47006
[72] Energy dependence of the scattering operator. Adv. Applied Math. 1 (1980) 300-323. · Zbl 0445.47007
[73] Metastable states of molecules. Commun. Math. Phys. 75 (1980) 263-283. · Zbl 0436.49034
[74] Non-linear functionals in quantum mechanics. Lecture Notes, E.P.F. Lausanne, 1980.
[75] With M. D. Srinivas: Photon counting probabilities in quantum optics. Optica Acta 28 (1981) 981-996.
[76] Asymptotic modifications of dynamical semigroups on C -algebras. J. London Math. Soc. 24 (1981) 537-547. · Zbl 0439.46050
[77] With Ph. A. Martin: An approach to metastability in some ferromagnetic systems. Helv. Phys Acta 54 (1981) 106-130.
[78] Symmetry breaking for molecular open systems. Ann. Inst. H. Poincare 35A (1981) 149-171. · Zbl 0493.49040
[79] Metastable states of symmetric Markov semigroups I. Proc. London Math. Soc. 45 (1982) 133-150. · Zbl 0498.47017
[80] Metastability and the Ising model. J. Stat. Phys. 27 (1982) 657-675. · Zbl 0511.60095
[81] Metastable states of symmetric Markov semigroups II. J. London Math. Soc. 26 (1982) 541-556. · Zbl 0527.47028
[82] Energy dependence of the scattering operator II. Commun. Math. Phys. 86 (1982) 149-160. · Zbl 0526.47002
[83] Stability of molecular eigenstates. Proc. Berlin IAMP Conference, 1981.
[84] The twisting trick for double well Hamiltonians. Commun. Math. Phys. 85 (1982) 471-479. · Zbl 0524.47019
[85] JWKB and related bound on Schrödinger eigenfunctions. Bull. London Math. Soc. 14 (1982) 273-284. · Zbl 0525.35026
[86] With M. D. Srinivas: What are the photon counting probabilities for open systems -a reply to Mandel’s comments. Optica Acta 29 (1982) 235-238.
[87] Some norm bounds and quadratic form inequalities for Schrödinger operators. J. Oper. Theory 9 (1983) 147-162. · Zbl 0516.47025
[88] Dynamical stability of metastable states. J. Func. Anal. 46 (1982) 373-386. · Zbl 0492.60072
[89] The harmonic functions of mean ergodic Markov semigroups. Math. Zeit. 181 (1982) 543-552. · Zbl 0493.60078
[90] With C. J. K. Batty: Positive semigroups and resolvents. J. Oper. Theory 10 (1983) 357-363. · Zbl 0529.47026
[91] Hypercontractive and related bounds for double well Schrödinger operators. Quart. J. Math. (2), 34 (1983) 407-421. · Zbl 0546.34021
[92] An adiabatic theorem applicable to the Stark effect. Commun. Math. Phys. 89 (1983) 329-339. · Zbl 0522.35086
[93] Spectral properties of metastable Markov semigroups. J. Funct. Anal. 52 (1983) 315-329. · Zbl 0525.47030
[94] Double well hamiltonians. Proc. London Math. Soc. 49 (1984) 193-206. · Zbl 0561.47021
[95] Some norm bounds and quadratic form inequalities for Schrödinger operators II. J. Oper. Theory 12 (1984) 177-196. · Zbl 0567.47006
[96] The rate of resolvent and semigroup convergence. Quart. J. Math. Oxford (2), 35 (1984) 121-130. · Zbl 0544.47033
[97] With B. Simon: Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians. Journal of Funct. Anal. 59 (1984) 335-395. · Zbl 0568.47034
[98] A generation theorem for operators commuting with group actions. Math Proc. Camb. Phil. Soc. 96 (1984) 313-320. · Zbl 0567.47038
[99] With B. Simon: Ultracontractive semigroups and some problems in analysis. Aspects of Math. and its Appl., A. Festschrift in honour of L. Nachbin Vol. 34 ed. J. A. Barroso: Elsevier Science Publ. B.V. 1986, 265-280. · Zbl 0638.47044
[100] Trace properties of the Dirichlet Laplacian. Math. Zeit. 188 (1985) 245-251. · Zbl 0573.35072
[101] With Pl. Muthuramalingam: Trace properties of some highly anisotropic oper-ators. Jour. of London Math. Soc. (2), 31 (1985) 137-149. · Zbl 0619.47006
[102] Structural isomers, double wells, resonances and Dirichlet decoupling. Annals of Physics 157 (1984) 166-182. · Zbl 0555.35027
[103] The eigenvalue distribution of degenerate Dirichlet forms. J. Diff. Eqns. 60 (1985) 103-130. · Zbl 0578.35075
[104] The asymptotic distribution and lower bounds to the spectrum for some singular elliptic operators. CIRM Colloquium, Luminy 1984, eds. B. Helffer and D. Robert, Publ. de l’Universite de Nantes, 1985, 37-42.
[105] With B. Simon: L 1 -properties of intrinsic Schrödinger semigroups. J. Funct. Anal. 65 (1986) 126-146. · Zbl 0613.47039
[106] Criteria for ultracontractivity. Ann. Inst. H. Poincare 43A (1985) 181-194. · Zbl 0589.35030
[107] L 1 -properties of second order elliptic operators. Bull. London Math. Soc. 17 (1985) 417-436. · Zbl 0583.35032
[108] Heat kernel bounds for second order elliptic operators on Riemannian mani-folds. Amer. J. Math. 109 (1987) 545-570. · Zbl 0648.58037
[109] Perturbations of ultracontractive semigroups. Quart. J. Math. (2), 37 (1986) 167-176. · Zbl 0614.47035
[110] Spectral properties of some second order elliptic operators on L p spaces. Proc. Symp on Aspects of Positivity in Functional Analysis, 1985. Eds. M. Wolff, R. Nagel. and U Schlotterbeck. North-Holland, 1986, 41-48. · Zbl 0618.35081
[111] Explicit constants for Gaussian upper bounds on heat kernels. Amer. J. Math. 109 (1987) 319-334. · Zbl 0659.35009
[112] With E. M. Harrell II. Conformally flat Riemannian metrics, Schrödinger oper-ators and semiclassical approximations. J. Diff. Eqns. 66 (1987) 165-188. · Zbl 0616.34020
[113] The equivalence of certain heat kernel and Green function bounds. J. Functional Anal. 71 (1987) 88-103. · Zbl 0652.35023
[114] With M. M. H. Pang. The Cauchy Problem and a generalization of the Hille-Yosida theorem. Proc. London Math. Soc. (3) 55 (1987) 181-208. · Zbl 0651.47026
[115] With N. Mandouvalos. Heat kernel bounds on manifolds with cusps. J. Functional Analysis 75 (1987) 311-322. · Zbl 0629.53044
[116] Kernel estimates for functions of second order elliptic operators. Quart. J. Math. Oxford (2) 39 (1988) 37-46. · Zbl 0652.35024
[117] With B. Simon and M. Taylor. L p spectral theory of Kleinian groups. J. Functional Anal. 78 (1988) 116-136. · Zbl 0644.58022
[118] Lipschitz continuity of functions of operators in the Schatten classes. J. London Math. Soc. 37 (1988) 148-157. · Zbl 0648.47011
[119] Gaussian upper bounds for the heat kernels of some second order operators on Riemannian manifolds. J. Functional Anal. 80 (1988) 16-32. · Zbl 0759.58045
[120] With N. Mandouvalos. heat kernel bounds on hyperbolic space and Kleinian groups. Proc. London Math. Soc. (3) 57 (1988) 182-208. · Zbl 0643.30035
[121] With M. M. H. Pang: Sharp heat kernel bounds for some Laplace operators. Quart. J. Math, Oxford (2), 40 (1989) 281-290. · Zbl 0701.35004
[122] With O. S. Rothaus: Markov semigroups on C -bundles. J. Functional Anal. 85 (1989) 264-286. · Zbl 0694.46049
[123] Pointwise bounds on the space and time derivatives of heat kernels. J. Oper. Theory 21 (1989) 367-378. · Zbl 0702.35106
[124] An eigenvalue bound for compact manifolds with varying curvature. Ann. Global Anal. and Geom. 7 (1989) 107-114. · Zbl 0685.53036
[125] With O. S. Rothaus: A BLW inequality for vector bundles and applications to spectral bounds. J. Functional Anal. 86 (1989) 390-410. · Zbl 0696.58046
[126] With A. Abdessemed: Some commutator estimates in the Schatten classes. J. London Math. Soc. (2) 39 (1989) 299-308. · Zbl 0692.47009
[127] Spectral properties of compact manifolds and changes of metric. Amer. J. Math. 112 (1990) 15-39. · Zbl 0691.53031
[128] With M. van den Berg: Heat flow out of regions in R m . Math. Zeit. 202 (1989) 463-482. · Zbl 0661.35040
[129] Pointwise inequalities for heat kernels, pp. 361-364, in IXth Inter. Congress in Math. Physics, Swansea, 1988, eds. B. Simon, A. Truman, I. M. Davies; IOP Publishing Ltd. 1989. · Zbl 0729.47030
[130] The hyperbolic geometry and spectrum of irregular domains. Nonlinearity 3 (1990) 913-945. · Zbl 0709.58038
[131] With L. Gross and B. Simon: Hypercontractivity: A Bibliographic Review. Ideas and Methods in Quantum and Statistical Mechanics, pp. 370-389 in eds. S. Albeverio et al., Volume 2, Camb. University Press, 1992. · Zbl 0790.46055
[132] With M. M. H. Pang: The eigenvalue gap for second order elliptic operators with Dirichlet boundary conditions. J. Diff. Eqns. 88 (1990) 46-90. · Zbl 0716.35057
[133] With B. Simon: Spectral properties of the Neumann Laplacian of Horns. Geometric and Functional Analysis. 2 (1992) 105-117. · Zbl 0749.35024
[134] Heat kernel bounds, conservation of probability and the Feller property. J. d’Analyse Math. 58 (1992) 99-119. · Zbl 0808.58041
[135] With B. Simon: L p norms of non-critical Schrödinger semigroups. J. Functional Anal. 102 (1991) 95-115. · Zbl 0743.47047
[136] Heat kernels in one dimension. Quart. J. Math. Oxford (2) 44 (1993) 283-299. · Zbl 0830.34019
[137] The state of the art for heat kernel bounds on negatively curved manifolds. Bull. London Math. Soc. 25 (1993) 289-292. · Zbl 0802.58053
[138] With J. M. Lindsay: Non-commutative symmetric Markov semigroups. Math. Zeit. 210 (1992) 379-411. · Zbl 0761.46051
[139] Large deviations for heat kernels on graphs. J. London Math. Soc. 47 (1993) 65-72. · Zbl 0799.58086
[140] Analysis on graphs and noncommutative geometry. J. Functional Analysis, 111 (1993) 398-430. · Zbl 0793.46043
[141] Two-dimensional Riemannian manifolds with fractal boundaries. J. London Math. Soc. (2) 49 (1994) 343-356. · Zbl 0824.58043
[142] With J. M. Lindsay: Superderivations and symmetric Markov semigroups. Commun. Math. Phys. 157 (1993) 359-370. · Zbl 0799.46081
[143] Eigenvalue stability bounds via weighted Sobolev spaces. Math. Zeit. 214 (1993) 357-371. · Zbl 0799.58082
[144] The Functional Calculus. J. London Math. Soc. (2) 55 (1995) 166-176. · Zbl 0858.47012
[145] With M. Lianantonakis: Heat kernel and Hardy estimates for locally Euclidean manifolds with fractal boundaries. Geom. and Funct. Anal. 3 (1993) 527-563. · Zbl 0797.58087
[146] The Hardy constant. Quart. J. Math. Oxford (2), 46 (1995) 417-431. · Zbl 0857.26005
[147] L p spectral independence and L 1 analyticity. J. London Math. Soc. (2) 52 (1995) 177-184. · Zbl 0913.47032
[148] Uniformly elliptic operators with measurable coefficients. J. Functional Anal. 132 (1995) 141-169. · Zbl 0839.35034
[149] Non-Gaussian aspects of heat kernel behaviour. J. London Math. Soc. (2) 55 (1997) 105-125. · Zbl 0879.35064
[150] Long time asymptotics of fourth order parabolic equations. J. d’Analyse Math. 67 (1995) 323-345. · Zbl 0851.35018
[151] Nonlinear Schrödinger operators and molecular structure. J. Phys. A, Math. Gen. 28 (1995) 4025-4041. · Zbl 0861.47049
[152] Heat kernel bounds for higher order elliptic operators. pp. III.1-III.11, Journées “Équations aux dérivées partielle”, Proceedings Saint Jean de Monts, May/June 1995. Groupement de Recherche CNRS, no. 1151, Rennes, 1995. ISBN 2-73-02-0331.
[153] With G. Barbatis: Sharp bounds on heat kernels of higher order uniformly ellip-tic operators. J. Oper. Theory 36 (1996) 179-198. · Zbl 0869.35048
[154] L p spectral independence for certain uniformly elliptic operators. pp. 122-125 in “Partial Differential Equations in Mathematical Physics”, eds. L. Hörmander and A. Melin. Birkhauser, 1996. · Zbl 0864.35077
[155] With A. M. Hinz: Explicit constants for Rellich inequalities in L p . /. Math. Zeit. 227 (1998) 511-523. · Zbl 0903.58049
[156] With A. M. Hinz: Kato class potentials for higher order elliptic operators. J. London Math. Soc. (2) 58 (1998) 669-678. · Zbl 0942.35063
[157] With L. Parnovski: Trapped modes in acoustic waveguides. Quart. J. Mech. and Appl. Math. 51 (1998) 477-492. · Zbl 0908.76083
[158] Limits on L p regularity of self-adjoint elliptic operators. J. Diff. Eqns. 135 (1997) 83-102. · Zbl 0871.35020
[159] L p spectral theory of higher order elliptic differential operators. Bull. London Math. Soc. 29 (1997) 513-546. · Zbl 0955.35019
[160] Spectral enclosures and complex resonances for general self-adjoint operators. LMS J. Comput. Math. 1 (1998) 42-74. · Zbl 0931.47021
[161] Pointwise lower bounds on the heat kernels of higher order elliptic operators. Math. Proc. Camb. Phil. Soc. 125 (1999) 105-111. · Zbl 0926.35032
[162] Ground state energy of almost periodic Schrödinger operators. Ergodic Theory and Dynamical Systems 19 (1999) 591-609. · Zbl 1018.47026
[163] A hierarchical method for obtaining eigenvalue enclosures. Math. of Comp. 69 (2000) 1435-1455. · Zbl 0958.34067
[164] Pseudospectra of differential operators. J. Operator Theory 43 (2000) 243-262. · Zbl 0998.34067
[165] Pseudospectra, the harmonic oscillator and complex resonances. Proc. R. Soc. London A, 455 (1999) 585-599. · Zbl 0931.70016
[166] Semi-classical states for non-self-adjoint Schrödinger operators. Commun. Math. Phys. 200 (1999) 35-41. · Zbl 0921.47060
[167] Sharp boundary estimates for elliptic operators. Math. Proc. Camb. Phil. Soc. 129 (2000) 165-178. · Zbl 0963.35146
[168] A review of Hardy inequalities. in “Conference in honour of V. G. Maz”ya, Ros-tock, 1998”. Operator Theory: Advances and Applications, vol.110, Birkhauser Verlag, Basel, 1999.
[169] The computation of thresholds for Schrödinger operators. LMS J. Comput. Math. 2 (1999) 139-154. · Zbl 1004.35035
[170] Computational spectral theory. pp. 76-94 in “Spectral Theory and Geometry”, eds. E. B. Davies and Y. Safarov. London Math. Soc. Lecture Note Series no. 273. Cambridge University Press, Cambridge, 1999. · Zbl 0952.47004
[171] With A. Aslanyan: Spectral instability for some Schrödinger operators. Numerische Mathematik 85 (2000) 525-552. · Zbl 0964.65076
[172] Wild spectral behaviour of anharmonic oscillators. Bull. London Math. Soc. 32 (2000) 432-438. · Zbl 1043.47502
[173] With B. M. Brown, P. J. Jimack, and M. D. Mihajlovic: A numerical investiga-tion of the solution of a class of fourth order eigenvalue problems. Proc. Roy. Soc. London A 456 (2000) 1505-1521. · Zbl 0977.65101
[174] With A. Aslanyan: On eigenfunction approximations for typical non-self-adjoint Schrödinger operators. Proc. Roy. Soc. London A 456 (2000) 1291-1303. · Zbl 1024.34077
[175] With A. A. Abramov and A. Aslanyan: Bounds on complex eigenvalues and resonances. J. Phys. A, 34 (2001) 57-72. · Zbl 1123.81415
[176] Spectral properties of random non-self-adjoint matrices and operators. Proc. Roy. Soc. London A 457 (2001) 191-206. · Zbl 1014.47002
[177] Spectral Theory of Pseudo-ergodic Operators. Commun. Math. Phys. 216 (2001) 687-704. · Zbl 1044.47031
[178] With V. I. Burenkov: Spectral stability of the Neumann Laplacian. J. Diff. Eqns. 186 (2002) 485-508. · Zbl 1042.35035
[179] With G. M. L. Gladwell, J. Leydold and P. F. Stadler: Discrete nodal domain theorems. Linear Alg. and Applic. 336 (2001) 51-60. · Zbl 0990.05093
[180] Building infinite machines. Brit. J. Phil. Sci. 52 (2001) 671-682. · Zbl 1020.03004
[181] Empiricism in Arithmetic and Analysis. Philosophia Mathematica (3) 11 (2003) 53-66. · Zbl 1047.00003
[182] With M. Lambrou: On the law of implication. Crux Mathematicorum with Mathematical Mayhem. 25 no. 8 (1999) 525-528.
[183] With Jiban Nath: Schrödinger operators with slowly decaying potentials. J. Comp. Appl. Math. 148 (2002) 1-28. · Zbl 1019.34083
[184] The Newtonian myth. Stud. Hist. Phil. Sci. 34 (2003) 763-780.
[185] Errata, Stud. Hist. Phil. Sci. 35 (2004) 413.
[186] With A. Aslanyan: Separation of variables in deformed cylinders. J. Comput. Phys. 174 (2001) 327-344. · Zbl 0991.65115
[187] Eigenvalues of an elliptic system. Math. Zeit. 243 (2003) 719-743. · Zbl 1032.34078
[188] Non-self-adjoint differential operators. Bull. London Math. Soc. 34 (2002) 513-532. · Zbl 1052.47042
[189] Quantum mechanics does not require the continuity of space. Stud. Hist. Phil. Mod. Phys. 34 (2003) 319-328. · Zbl 1222.81052
[190] With M. Plum: Spectral pollution. IMA J. Numer. Anal. 24 (2004) 417-438. · Zbl 1062.65056
[191] Semigroup growth bounds. J. Oper. Theory 53:2 (2005) 225-249. · Zbl 1114.47040
[192] Some remarks on the foundations of quantum mechanics. Brit. J. Phil. Sci. 56 (2005) 521-539. · Zbl 1152.81654
[193] With A. Kuijlaars: Spectral asymptotics of the non-self-adjoint harmonic oscillator. J. London Math. Soc. (2) 70 (2004) 420-426. · Zbl 1073.34093
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[224] Some PhD students and PostDocs David E Evans, DPhil., Oxford 1975
[225] Peter F Palmer, DPhil., Oxford 1977
[226] Greg Singleton, Ph.D., King’s College London, awarded 1986
[227] Michael Pang, Ph.D., King’s College London, awarded 1988, then postdoc until 1991
[228] Maria Lianantonakis, Ph.D., King’s College London, awarded 1990, then postdoc until 1993
[229] Gerassimos Barbatis, Ph.D., King’s College London, awarded 1994, then postdoc until 1997
[230] Mark Owen, Ph.D., King’s College London, awarded 1997
[231] Owen Nicholas, Ph.D., King’s College London, awarded 2000
[232] Narinder Claire, Ph.D., King’s College London, awarded 2000
[233] Lyonell Boulton, Ph.D., King’s College London, awarded 2001, postdoc March 1-July 31, 2001
[234] Anna Aslanyan, Postdoc at King’s College London, June 1997 to December 31, 2000
[235] Paul Redparth, Ph.D., King’s College London, awarded 2001
[236] Jiban Nath, Ph.D., King’s College London, awarded 2002
[237] Colin Mason, Ph.D., King’s College London, awarded 2002
[238] Carmen Martinez, Ph.D., King’s College London, awarded 2005
[239] My Long Tham, Ph.D., King’s College London, awarded 2008
[240] James Hinchcliffe, Ph.D., King’s College London, awarded 2008
[241] Paul Incani, Ph.D., King’s College London, awarded 2009
[242] John Weir, Ph.D., King’s College London, awarded 2010 See also in the Mathematical Genealogy Project 3 .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.