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Principal Submodules in the Module of Entire Functions, Which is Dual to the Schwarz Space, and Weak Spectral Synthesis in the Schwartz Space

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Abstract

We obtain a sufficient condition of the weak localizability of a principal submodule in the module of entire functions of exponential type and polynomial growth on the real line. Applications to the problem of the (weak) spectral synthesis in the Schwartz space C∞ (a; b) are discussed.

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Authors and Affiliations

  1. Bashkir State University, Ufa, Russia

    N. F. Abuzyarova

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  1. N. F. Abuzyarova
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Correspondence to N. F. Abuzyarova.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 142, Complex Analysis, 2017.

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Abuzyarova, N.F. Principal Submodules in the Module of Entire Functions, Which is Dual to the Schwarz Space, and Weak Spectral Synthesis in the Schwartz Space. J Math Sci 241, 658–671 (2019). https://doi.org/10.1007/s10958-019-04453-0

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  • DOI: https://doi.org/10.1007/s10958-019-04453-0

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