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On non-degeneracy of the ground state of Schrödinger operators. (English) Zbl 0353.35032


MSC:

35J10 Schrödinger operator, Schrödinger equation
35P15 Estimates of eigenvalues in context of PDEs
47F05 General theory of partial differential operators
47B25 Linear symmetric and selfadjoint operators (unbounded)

References:

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[12] Hoegh-Krohn, R., Simon, B.: Hypercontractive Semigroups and Two Dimensional Self-Coupled Bose Fields. J. Functional Analysis9, 121–180 (1972) · Zbl 0241.47029 · doi:10.1016/0022-1236(72)90008-0
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[14] Kato, T.: Perturbation Theory for Linear Operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601
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[16] Perron, O.: Über Matrizen aus Nichtnegativen Elementen. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, 456–477 (1912) · JFM 43.0204.09
[17] Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. I: Functional Analysis. New York, London: Academic Press 1972 · Zbl 0242.46001
[18] Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. II: Fourier Analysis, Self-Adjointness. New York, London: Academic Press 1975 · Zbl 0308.47002
[19] Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. III: Analysis of Operators. New York, London: Academic Press (in preparation) · Zbl 0401.47001
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[21] Simon, B.: An Abstract Kato’s Inequality for Generators of Positivity Preserving Semigroups. Indiana Univ. Math. J. (to appear) · Zbl 0389.47021
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