Limiting absorption principle on $L^p$-spaces and scattering theory

Abstract

In this paper, we study the mapping property form $L^p$ to $L^q$ of the resolvent of the Fourier multiplier operators and scattering theory of generalized Schrödinger operators. Though the first half of the subject is studied in [4], we extend their result to away from the duality line and we also study the Hölder continuity of the resolvent.

arXiv comment32pages

References in corpus (6)

• Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations
• Carleman estimates and absence of embedded eigenvalues
• Inverse scattering at a fixed energy for discrere Schrödinger operators on the square lattice
• Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications
• Eigenvalue estimates for bilayer graphene
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Cited by in corpus (1)

• Counterexample to the Laptev--Safronov conjecture