Divergence-type operators: Spectral theory and spacetime estimates

Matania Ben-Artzi

doi:10.1007/978-3-0348-0454-7_1

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

2 Scopus citations

Abstract

The paper is concerned with various aspects of the spectral structure of the operator (Formula Presented.) It is assumed to be formally self-adjoint in L²(ℝⁿ),n ≥ 2. The real coefficients a_j,k(x)= a_k,j(x) are assumed to be bounded and H is assumed to be uniformly elliptic and to coincide with −∆ 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	Progress in Mathematics
Publisher	Springer Basel
Pages	1-40
Number of pages	40
DOIs	https://doi.org/10.1007/978-3-0348-0454-7_1
State	Published - 2012

Publication series

Name	Progress in Mathematics
Volume	301
ISSN (Print)	0743-1643
ISSN (Electronic)	2296-505X

Bibliographical note

Publisher Copyright:
© 2012, Springer Basel.

Keywords

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

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10.1007/978-3-0348-0454-7_1

Cite this

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Divergence-type operators: Spectral theory and spacetime estimates

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Keywords

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