Open Access
June 2011 Holomorphic families of Schrödinger operators in Lp
Yoshiki Maeda, Noboru Okazawa*
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SUT J. Math. 47(2): 185-216 (June 2011). DOI: 10.55937/sut/1328712856

Abstract

Given two m-sectorial operators in a reflexive Banach space X, a sufficient condition is presented for the family {T+κA;κΣc} to be holomorphic of type (A), where Σ is a closed convex region in the κ-plane such that Σ is the left branch of a hyperbola. The abstract formulation is almost identical with Kato’s when X is a Hilbert space. However, Σ is typically reduced to a parabola when X is a Hilbert space. The m-sectoriality is a generalized notion of the nonnegative selfadjointness so that Schrödinger operators with singular potentials in the Lp-spaces (1<p<) are typical examples of the abstract theory. In this connection a detailed analysis is given in the case of Δ+κ|x|2. This application is an Lp-generalization of Kato’s.

Acknowledgments

The authors want to thank the referee for reading their manuscript carefully. Especially a lot of comments are helpful to make it as readable as possible.

Citation

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Yoshiki Maeda. Noboru Okazawa*. "Holomorphic families of Schrödinger operators in Lp." SUT J. Math. 47 (2) 185 - 216, June 2011. https://doi.org/10.55937/sut/1328712856

Information

Received: 11 May 2011; Revised: 16 November 2011; Published: June 2011
First available in Project Euclid: 11 June 2022

Digital Object Identifier: 10.55937/sut/1328712856

Subjects:
Primary: 35J10 , 47A55 , 47A56 , 47B44

Keywords: Closed linear operators , duality maps , holomorphic families of type (A) , m-accretive operators , m-sectorial operators , Schrödinger operators

Rights: Copyright © 2011 Tokyo University of Science

Vol.47 • No. 2 • June 2011
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