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November/December 2020 Spectral identities and smoothing estimates for evolution operators
Matania Ben-Artzi, Michael Ruzhansky, Mitsuru Sugimoto
Adv. Differential Equations 25(11/12): 627-650 (November/December 2020).

Abstract

Smoothing (and decay) spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the existence (and weak continuity) of the spectral density in a functional setting. Spectral identities for the time evolution of such operators are derived, enabling results concerning “best constants” for smoothing estimates. When combined with suitable “comparison principles” (analogous to those established in [39]), they yield smoothing estimates for classes of functions of the operators.

An important contribution of this study involves the comparison of the spectral density of an operator $H$ and its perturbation $H+V.$ It entails a derivation of global spacetime estimates for $H+V$ on the basis of analogous estimates for $H.$

A number of applications are given, including smoothing estimates for fractional Laplacians, Stark Hamiltonians and Schrödinger operators with potentials.

Citation

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Matania Ben-Artzi. Michael Ruzhansky. Mitsuru Sugimoto. "Spectral identities and smoothing estimates for evolution operators." Adv. Differential Equations 25 (11/12) 627 - 650, November/December 2020.

Information

Published: November/December 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4173171

Subjects:
Primary: 35G10, 35S30, 47A10

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.25 • No. 11/12 • November/December 2020
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