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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

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Volume 6, Issue 1


Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization

A. R. Soltani / Z. Shishebor
Published Online: 2010-02-24 | DOI: https://doi.org/10.1515/GMJ.1999.91


Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {An } ⊂ be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (Spectral theory of periodically and quasi-periodically stationary SαS sequences, University of North Carolina, Chapel Hill, 1991). In this work we proceed further to characterize {An } by a positive measure μ and a number T of -valued functions a 0, . . . , a T–1; in the spectral form , where and Φ is an -valued Borel set function on [0, 2π) such that

(Φ(Δ)x, Φ(Δ′)x′) Y = (x, x′) X μ(Δ ∩ Δ′).

Key words and phrases.: Hilbert space; bounded linear operators; weakly periodic sequences; spectral representation

About the article

Received: 1996-12-18

Revised: 1997-09-05

Published Online: 2010-02-24

Published in Print: 1999-02-01

Citation Information: Georgian Mathematical Journal, Volume 6, Issue 1, Pages 91–98, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.1999.91.

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