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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 21, Issue 2

Issues

Spectral representation of a Banach-valued stationary random function on a locally compact abelian group

Tawfik Benchikh
  • Laboratoire de Statistique et Processus Stochastiques, Université Djillali Liabès, BP 89, Sidi Bel Abbés 22000, Algeria
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Published Online: 2014-05-17 | DOI: https://doi.org/10.1515/gmj-2014-0023

Abstract.

Let LE2 be a Banach space of all ℙ-square integrable random variables defined on some probability space (Ω,𝒜,) with values in the complex separable Banach space E. For an LE2-valued stationary continuous random function 𝔛=(Xg)gG on the locally compact abelian group G, we provide a condition of existence of a random measure Z taking values in LE2 such that (Xg)gG has a spectral representation as a Fourier transform of Z.

Keywords: Random measures; stationary random function; Fourier transform; stochastic integrals; spectral measures

MSC: 60G57; 60G10; 60H05; 60B15

About the article

Received: 2012-08-05

Revised: 2013-09-23

Accepted: 2014-02-28

Published Online: 2014-05-17

Published in Print: 2014-06-01


Funding Source: Agence Nationale de Recherche Universitaire (A.N.D.R.U.) in P.N.R.

Award identifier / Grant number: No. 46/1


Citation Information: Georgian Mathematical Journal, Volume 21, Issue 2, Pages 139–145, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2014-0023.

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