Abstract
The aim of this paper is to present results on the independence of the spectrum of Schrödinger operators in different spaces. We treat Schrödinger operators of a very general kind, namely - ½Δ perturbed by certain measures μ.
Presented at the meeting by J. Voigt
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References.
D. Alboth: Closable translation invariant operators and perturbations by potentials. Dissertation, Kiel 1991.
W. Arendt: Gaussian estimates and p-independence of the spectrum in Lp. Manuscript 1993.
A. G. Belyi, Yu. A. Semenov: Lp-theory of Schrödinger semigroups II. Sibirskii Matematicheskii Zhurnal 31, 16–26 (1990) (russian). Translation: Siberian Math. J. 31, 540-549 (1990).
J. M. Berezanski: Expansions in eigenfunctions of selfadjoint operators. Transi. Math. Monogr., vol. 17, Amer. Math. Soc, Providence, 1968.
P. L. Butzer, H. Berens: Semi-groups of operators and approximation. Springer-Verlag, Berlin, 1967.
R. Hempel, J. Voigt: The spectrum of a Schrödinger operator in L p(RN) is p-independent. Commun. Math. Phys. 104, 243–250 (1986).
R. Hempel, J. Voigt: On the L p-spectrum of Schrödinger operators. J. Math. Anal. Appl. 121, 138–159 (1987).
I. W. Herbst, A. D. Sloan: Perturbation of translation invariant positivity preserving semigroups on L 2(RN). Transactions Amer. Math. Soc. 236, 325–360 (1978).
E. Hllle, R. S. Phillips: Functional analysis and semi-groups. Amer. Math. Soc, Providence, 1957.
A. M. Hinz, G. Stolz: Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators. Math. Ann. 294, 195–211 (1992).
J. van Neerven: The adjoint of a semigroup of linear operators. Lecture Notes in Math. 1529, Springer-Verlag, Berlin, 1992.
Th. Poerschke, G. Stolz, J. Weidmann: Expansions in generalized eigenfunctions of self adjoint operators. Math. Z. 202, 397–408 (1989).
M. Reed, B. Simon: Methods of modern mathematical physics II: Fourier analysis, self-adjointness. Academic Press, New York, 1975.
G. Schreieck, J. Voigt: Stability of the Lp-spectrum of Schrödinger operators with form small negative part of the potential. In: “Functional Analysis”, Proc. Essen 1991, Bierstedt, Pietsch, Ruess, Vogt eds., Marcel Dekker, to appear.
I. Eh. Shnol’: Ob ogranichennykh resheniyakh uravneniya vtorogo poryadka v chastnykh proizvodnykh. Dokl. Akad. Nauk SSSR 89, 411–413 (1953).
M. A. Shubin: Spectral theory of elliptic operators on non-compact manifolds. In: “Méthodes semi-classiques, vol. 1”, Astérisque 207, 37–108 (1992).
B. Simon: Schrödinger semigroups. Bull. (N. S.) Amer. Math. Soc. 7, 447–526 (1982).
P. Stollmann, J. Voigt: Perturbation of Dirichlet forms by measures. Preprint 1992.
K.-Th. Sturm: On the Lp-spectrum of uniformly elliptic operators on Riemannian manifolds. J. Funct. Anal., to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Basel AG
About this chapter
Cite this chapter
Hempel, R., Voigt, J. (1994). The Spectrum of Schrödinger Operators in L p (R d) and in C 0(R d). In: Demuth, M., Exner, P., Neidhardt, H., Zagrebnov, V. (eds) Mathematical Results in Quantum Mechanics. Operator Theory: Advances and Applications, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8545-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8545-4_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9673-3
Online ISBN: 978-3-0348-8545-4
eBook Packages: Springer Book Archive