Toeplitz Operators with Frequency Modulated Semi-Almost Periodic Symbols

A. Böttcher, S. Grudsky, Ilya Spitkovsky

Research output: Contribution to journalArticle

Abstract

It is well known that amplitude modulation does not affect Fredholmness of Toeplitz operators. The same is true for frequency modulation provided the symbol of the operator is piecewise continuous. In this article, it is shown that frequency modulation can destroy Fredholmness for Toeplitz operators with almost periodic symbols; the corresponding example is based on the observation that certain almost periodic functions become semi-almost periodic functions after appropriate frequency modulation. Moreover, this article contains several results that can be employed in order to decide whether a Toeplitz operator with a frequency modulated semi-almost periodic symbol is Fredholm.

Original languageEnglish (US)
Pages (from-to)523-535
Number of pages13
JournalJournal of Fourier Analysis and Applications
Volume7
Issue number5
DOIs
StatePublished - Jan 1 2001

Fingerprint

Frequency Modulation
Toeplitz Operator
Almost Periodic
Frequency modulation
Fredholmness
Almost Periodic Functions
Amplitude Modulation
Amplitude modulation
Piecewise continuous
Operator

Keywords

  • Almostperiodic function
  • Fredholm operator
  • Frequency modulation
  • Semi-almost periodic function
  • Toeplitz operator

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

Toeplitz Operators with Frequency Modulated Semi-Almost Periodic Symbols. / Böttcher, A.; Grudsky, S.; Spitkovsky, Ilya.

In: Journal of Fourier Analysis and Applications, Vol. 7, No. 5, 01.01.2001, p. 523-535.

Research output: Contribution to journalArticle

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