×

Spectral theory for contraction semigroups on Hilbert space. (English) Zbl 0326.47038


MSC:

47D03 Groups and semigroups of linear operators
47A10 Spectrum, resolvent
47A20 Dilations, extensions, compressions of linear operators
Full Text: DOI

References:

[1] R. G. Douglas, P. S. Muhly, and Carl Pearcy, Lifting commuting operators, Michigan Math. J. 15 (1968), 385 – 395. · Zbl 0174.18202
[2] Paul A. Fuhrmann, On the corona theorem and its application to spectral problems in Hilbert space, Trans. Amer. Math. Soc. 132 (1968), 55 – 66. · Zbl 0187.38002
[3] Paul A. Fuhrmann, A functional calculus in Hilbert spaces based on operator valued analytic functions, Israel J. Math. 6 (1968), 267 – 278. · Zbl 0187.38003 · doi:10.1007/BF02760259
[4] L. Gearhart, On the spectral theory of the translation semigroup and its commutant, Thesis, Univ. of Illinois, Chicago, 1975.
[5] Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102 – 112. · Zbl 0107.09802 · doi:10.1515/crll.1961.208.102
[6] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[7] Peter D. Lax, Translation invariant spaces, Acta Math. 101 (1959), 163 – 178. · Zbl 0085.09102 · doi:10.1007/BF02559553
[8] Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. · Zbl 0186.16301
[9] James W. Moeller, On the spectra of some translation invariant spaces, J. Math. Anal. Appl. 4 (1962), 276 – 296. · Zbl 0116.32301 · doi:10.1016/0022-247X(62)90055-0
[10] J. W. Moeller, Translation invariant spaces with zero-free spectra, Duke Math. J. 31 (1964), 99 – 108. · Zbl 0187.37902
[11] R. S. Phillips, Spectral theory for semi-groups of linear operators, Trans. Amer. Math. Soc. 71 (1951), 393 – 415. · Zbl 0045.21502
[12] Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, Translated from the French and revised, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. · Zbl 0201.45003
[13] Béla Sz.-Nagy and Ciprian Foiaş, On the structure of intertwining operators, Acta Sci. Math. (Szeged) 35 (1973), 225 – 254. · Zbl 0272.47010
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.