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Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2011, Issue 8(89), Pages 37–44 (Mi vsgu121)  

Mathematics

The system of shifts of functions

E. S. Klimova

Dept. of Functional Analysis and Theory of Functions, Samara State University, Samara, 443011, Russian Federation.

Abstract: The system of shift of functions $(T_{\lambda _{k}}g(x))_{n\in \mathbb{Z}}$ in $L^{2}(\mathbb{R})$ space is considered in this paper, where $\lambda_{n}\in \mathbb{R}$. We find conditions on real sequence $(\lambda_{n})$ which provide such properties of the system as to be a frame, Bessel system, complete sequence in the space $L^{2}(\mathbb{R})$.

Keywords: Bessel sequence, frame, shift operator, complete systems.

Full text: PDF file (574 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file
UDC: 517.51+517.98
Received: 22.03.2011
Revised: 22.03.2011

Citation: E. S. Klimova, “The system of shifts of functions”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2011, no. 8(89), 37–44

Citation in format AMSBIB
\Bibitem{Kli11}
\by E.~S.~Klimova
\paper The system of shifts of functions
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2011
\issue 8(89)
\pages 37--44
\mathnet{http://mi.mathnet.ru/vsgu121}


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