Abstract
LetH p =−1/2Δ+V denote a Schrödinger operator, acting inL p ℝv, 1≦p≦∞. We show that σ(H p )=σ(H 2) for allp∈[1, ∞], for rather general potentialsV.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aizenman, M., Simon, B.: Brownian motion and Harnack inequality for Schrödinger operators. Commun. Pure Appl. Math.35, 209–273 (1982)
Auterhoff, J.: Interpolationseigenschaften des Spektrums linearer Operatoren aufL P -Räumen. Math. Z.184, 397–406 (1983)
Devinatz, A.: Schrödinger operators with singular potentials. J. Oper. Theory4, 25–35 (1980)
Dunford, N., Pettis, B. J.: Linear operations on summable functions. Trans. Am. Math. Soc.47, 323–392 (1940)
Hempel, R., Voigt, J.: On theL p-spectrum of Schrödinger operators. J. Math. Anal. Appl. (to appear)
Jörgens, K.: Lineare Integraloperatoren. Stuttgart: B. G. Teubner, 1970
Kato, T.: Perturbation theory for linear operators. Second edition. Berlin Heidelberg, New York: Springer 1976
Reed, M., Simon, B.: Methods of modern mathematical physics I: Functional analysis. Revised and enlarged edition. New York: Academic Press 1980
Reed, M., Simon, B.: Methods of modern mathematical physics II: Fourier analysis, self-adjointness. New York: Academic Press 1975
Sigal, I. M.: A generalized Weyl theorem andL P -spectra of Schrödinger operators. Preprint
Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979
Simon, B.: Brownian motion,L P properties of Schrödinger operators and the localization of binding. J. Funct. Anal.35, 215–225 (1980)
Simon, B.: Schrödinger semigroups. Bull. Am. Math. Soc. New Ser.7, 447–526 (1982)
Voigt, J.: Absorption semigroups, their generators, and Schrödinger semigroups, J. Funct. Anal. (to appear)
Author information
Authors and Affiliations
Additional information
Communicated by B. Simon
Rights and permissions
About this article
Cite this article
Hempel, R., Voigt, J. The spectrum of a Schrödinger operator inL p ℝv isp-independent. Commun.Math. Phys. 104, 243–250 (1986). https://doi.org/10.1007/BF01211592
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01211592