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Mat. Zametki, 2006, Volume 79, Issue 4, Pages 581–596 (Mi mz2728)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalized Fourier transform and its applications

S. V. Panyushkin

Orel State University

Abstract: We consider the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space. We give a definition of this operator and establish its basic properties. Special attention is paid to cases in which the range of the generalized Fourier transform coincides with a weighted space of entire functions. The results are applied to finding the orders and types of operators in various spaces.

DOI: https://doi.org/10.4213/mzm2728

Full text: PDF file (250 kB)
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English version:
Mathematical Notes, 2006, 79:4, 537–550

Bibliographic databases:

UDC: 517.55
Received: 08.04.2004

Citation: S. V. Panyushkin, “Generalized Fourier transform and its applications”, Mat. Zametki, 79:4 (2006), 581–596; Math. Notes, 79:4 (2006), 537–550

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. I. Karamov, V. V. Napalkov, “Generalized Dunkl operator”, Ufa Math. J., 6:1 (2014), 56–65  mathnet  crossref  isi  elib
    2. S. N. Mishin, “Invariance of the Order and Type of a Sequence of Operators”, Math. Notes, 100:3 (2016), 429–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математические заметки Mathematical Notes
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