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2006•Proceedings of the American Mathematical SocietyOpen access

Further results on the connectivity of Parseval frame wavelets

Gustavo Garrigós, Eugenio Hernández, Hrvoje Šikić, Fernando Soria

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Abstract

In a previous paper, the authors introduced new ideas to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.

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What this paper is about

In a previous paper, the authors introduced new ideas to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In a previous paper, the authors introduced new ideas to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.

Key concepts: Parseval's theorem, Class (philosophy), Frame (networking), Mathematics, Set (abstract data type), Pure mathematics, Fourier analysis, Computer science

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