Divergence-type operators: Spectral theory and spacetime estimates

Matania Ben-Artzi

doi:10.1007/978-3-0348-0454-7

Divergence-type operators: Spectral theory and spacetime estimates

Matania Ben-Artzi^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

The paper is concerned with various aspects of the spectral structure of the operator. It is assumed to be formally self-adjoint in L²,(Rⁿ), n≥2. The real coefficients a^j,^k(x)= a^j,^k(x) are assumed to be bounded and H is assumed to be uniformly elliptic and to coincide with -Δ outside of a ball. A Limiting Absorption Principle (LAP) is proved in the framework of weighted Sobolev spaces. It is then used for (i) A general eigenfunction expansion theorem and (ii) Global spacetime estimates for the associated (inhomogeneous) generalized wave equation.

Original language	English
Title of host publication	Evolution Equations of Hyperbolic and Schrödinger Type
Subtitle of host publication	Asymptotics, Estimates and Nonlinearities
Publisher	Springer Basel
Pages	1-40
Number of pages	40
ISBN (Electronic)	9783034804547
ISBN (Print)	9783034804530
DOIs	https://doi.org/10.1007/978-3-0348-0454-7
State	Published - 1 Jan 2012

Bibliographical note

Publisher Copyright:
© Springer Basel 2012. All rights reserved.

Keywords

Divergence-type operator
Eigenfunction expansion
Limiting absorption principle
Spacetime estimates
Spectral derivative

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10.1007/978-3-0348-0454-7

Cite this

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Divergence-type operators: Spectral theory and spacetime estimates

Abstract

Bibliographical note

Keywords

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