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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 2, Pages 201–224 (Mi izv332)  

This article is cited in 5 scientific papers (total in 5 papers)

A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces

A. Yu. Khrennikov, H. Petersson


Abstract: We study entire functions on infinite-dimensional spaces. The basis is the study of spaces of Gateaux holomorphic functions that are bounded on certain subsets (bounded entire functions). The main goal is to characterize the Fourier image of the corresponding spaces of generalized entire functions (ultra-distributions) by an infinite-dimensional Paley–Wiener theorem. We introduce entire functions of exponential type and prove a generalization of the classical Paley–Wiener theorem. The crucial point of our theory is the dimension-invariant estimate given by Lemma 4.12.

DOI: https://doi.org/10.4213/im332

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English version:
Izvestiya: Mathematics, 2001, 65:2, 403–424

Bibliographic databases:

MSC: 46G20, 28C20
Received: 13.09.1999

Citation: A. Yu. Khrennikov, H. Petersson, “A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces”, Izv. RAN. Ser. Mat., 65:2 (2001), 201–224; Izv. Math., 65:2 (2001), 403–424

Citation in format AMSBIB
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\by A.~Yu.~Khrennikov, H.~Petersson
\paper A~Paley--Wiener theorem for generalized entire functions on infinite-dimensional spaces
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 2
\pages 201--224
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\crossref{https://doi.org/10.4213/im332}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1842845}
\zmath{https://zbmath.org/?q=an:1029.46054}
\elib{http://elibrary.ru/item.asp?id=14150271}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 2
\pages 403--424
\crossref{https://doi.org/10.1070/im2001v065n02ABEH000332}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746984907}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. Buskes, A. G. Kusraev, “Representation and extension of orthoregular bilinear operators”, Vladikavk. matem. zhurn., 9:1 (2007), 16–29  mathnet  mathscinet  elib
    2. V. P. Kondakov, “O differentsiruemosti otobrazhenii i stroenii prostranstv golomorfnykh funktsii na beskonechnomernykh prostranstvakh”, Vladikavk. matem. zhurn., 9:2 (2007), 9–21  mathnet  mathscinet  elib
    3. A. Yu. Khrennikov, “Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals”, Izv. Math., 72:1 (2008), 127–148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. P. Kondakov, “O bazisakh v prostranstvakh nepreryvnykh $n$-odnorodnykh polinomov, deistvuyuschikh v yadernykh prostranstvakh Kete”, Vladikavk. matem. zhurn., 14:2 (2012), 39–44  mathnet
    5. Belyaev A.A., Smolyanov O.G., “Distributions and Analytical Measures on Infinite-Dimensional Spaces”, Dokl. Math., 98:3 (2018), 541–544  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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