Pseudodifferential operators with heavy spectrum

A. Böttcher, Ilya Spitkovsky

Research output: Contribution to journalArticle

Abstract

We establish Fredholm criteria and index formulas for one-dimensional zero-order pseudodifferential operators with piecewise continuous generating functions on Lp spaces with Muckenhoupt weights. The Fredholm symbol of such operators is shown to be a matrix function defined on a set which, roughly speaking, is a cylinder with a certain collection of horn shaped handles. The presence of these horns implies that, unlike the case of Lp spaces without weight or with so-called power weights, the spectrum may contain heavy parts, i. e. the set of the interior points of the spectrum need not be empty. Our proof makes essential use of recent results by Finck, Roch, Silbermann, Gohberg, and Krupnik on the inverse closedness of certain Banach algebras.

Original languageEnglish (US)
Pages (from-to)251-269
Number of pages19
JournalIntegral Equations and Operator Theory
Volume19
Issue number3
DOIs
StatePublished - Sep 1 1994

Fingerprint

Lp Spaces
Pseudodifferential Operators
Muckenhoupt Weights
Piecewise continuous
Matrix Function
Interior Point
Banach algebra
Generating Function
Continuous Function
Imply
Zero
Operator

Keywords

  • AMS subject classification: 45E05, 45E10, 47A53, 47G30

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Cite this

Pseudodifferential operators with heavy spectrum. / Böttcher, A.; Spitkovsky, Ilya.

In: Integral Equations and Operator Theory, Vol. 19, No. 3, 01.09.1994, p. 251-269.

Research output: Contribution to journalArticle

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