Ulam Stability Problem for Frames

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 52)

Abstract

In this paper we give a solution to the Ulam stability problem for continuous Parseval frames in finite dimensional Hilbert spaces. We prove that if F is a nearly Parseval frame then there exists a Parseval frame near F. Also, we give generalizations of this result.

Keywords

Hyers–Ulam-Rassias stability Frames 

Notes

Acknowledgements

The first author was supported by the Grant: POSDRU/88/1.5/S/49516, project: “Creşterea calităţii şi competivităţii cercetării doctorale prin acordarea de burse.”

The authors thanks Professors J. Brzdȩk, P.G. Casazza, O. Christensen and Th.M. Rassias for carefully reading and useful comments.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics“Politehnica” University of TimişoaraTimişoaraRomania

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