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

    Böttcher, A. ; Grudsky, S. ; Spitkovsky, Ilya. / Toeplitz Operators with Frequency Modulated Semi-Almost Periodic Symbols. In: Journal of Fourier Analysis and Applications. 2001 ; Vol. 7, No. 5. pp. 523-535.
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