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On complete interpolating sequences and sampling expansions

Part of: Information and communication, circuits

Published online by Cambridge University Press:  01 January 2010

Kevin Smith
Kevin Smith*
Affiliation:
159 Thoday Street Cambridge, CB1 3AT, United Kingdom (email: [email protected])

Abstract

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Complete interpolating sequences for L2(−π,π) are considered under the condition that the real parts of the sequence are a subsequence of the scaled integers xℤ, x>0. It is found that this condition leads to very specific and restrictive conditions on the existence and structure of complete interpolating sequences for L2(−π,π). Further general results in the case of bunched sampling of Bernstein functions are also given.

MSC classification

Secondary: 94-02: Research exposition (monographs, survey articles)
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 1 - 9
Copyright
Copyright © London Mathematical Society 2010

References

[1] Higgins, J. R., Sampling theory in Fourier and signal analysis (Oxford University Press, New York, 1996).CrossRefGoogle Scholar
[2] Higgins, J. R., Completeness and basis properties of sets of special functions (Cambridge University Press, Cambridge, 1977).CrossRefGoogle Scholar
[3] Kadec, M. I., ‘On the exact value of the Paley–Wiener constant’, Dokl. Acad. Nauk SSSR 155 (1964) 1253–1254Soviet Math. Dokl. 5 (1964) 559–561.Google Scholar
[4] Young, R. M., An introduction to non-harmonic Fourier series (Academic Press, New York, 1980).Google Scholar