Carathéodory-toeplitz and nehari problems for matrix valued almost periodic functions

Leiba Rodman, Ilya Spitkovsky, Hugo J. Woerdeman

    Research output: Contribution to journalArticle

    Abstract

    In this paper the positive and strictly contractive extension problems for almost periodic matrix functions are treated. We present necessary and sufficient conditions for the existence of extensions in terms of Toeplitz and Hankel operators on Besicovitch spaces and Lebesgue spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property. A linear fractional parameterization of the set of all extensions is also provided. The techniques used in the proofs include factorizations of matrix valued almost periodic functions and a . general algebraic scheme called the band method.

    Original languageEnglish (US)
    Pages (from-to)2185-2227
    Number of pages43
    JournalTransactions of the American Mathematical Society
    Volume350
    Issue number6
    StatePublished - Dec 1 1998

    Fingerprint

    Almost Periodic Functions
    Otto Toeplitz
    Parameterization
    Factorization
    Entropy
    Factorization of Matrices
    Hankel Operator
    Toeplitz Operator
    Lebesgue Space
    Matrix Function
    Almost Periodic
    Maximum Entropy
    Periodic Functions
    Fractional
    Strictly
    Necessary Conditions
    Sufficient Conditions

    Keywords

    • Almost periodic matrix functions
    • Band method
    • Besicovitch space
    • Canonical factorization
    • Contractive extensions
    • Hankel operators
    • Positive extensions
    • Toeplitz operators

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Carathéodory-toeplitz and nehari problems for matrix valued almost periodic functions. / Rodman, Leiba; Spitkovsky, Ilya; Woerdeman, Hugo J.

    In: Transactions of the American Mathematical Society, Vol. 350, No. 6, 01.12.1998, p. 2185-2227.

    Research output: Contribution to journalArticle

    Rodman, Leiba ; Spitkovsky, Ilya ; Woerdeman, Hugo J. / Carathéodory-toeplitz and nehari problems for matrix valued almost periodic functions. In: Transactions of the American Mathematical Society. 1998 ; Vol. 350, No. 6. pp. 2185-2227.
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