One-dimensional dyadic wavelets / Peter M. Luthy, Hrvoje Šikić, Fernando Soria, Guido L. Weiss, Edward N. Wilson.

Format:

Book

Author/Creator:

Luthy, Peter M., 1983- author.

Šikić, Hrvoje, author.

Soria, Fernando, author.

Weiss, Guido, 1928-2021, author.

Wilson, Edward N., author.

Series:

Memoirs of the American Mathematical Society ; v. 1378.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 280, Number 1378

Language:

English

Subjects (All):

Wavelets (Mathematics).

Harmonic analysis.

Physical Description:

ix, 152 pages : illustrations ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, [2022]

Summary:

"The theory of wavelets has been thoroughly studied by many authors; standard references include books by I. Daubechies, by Y. Meyer, by R. Coifman and Y. Meyer, by C.K. Chui, and by M.V. Wickerhauser. In addition, the development of wavelets influenced the study of various other reproducing function systems. Interestingly enough, some open questions remained unsolved or only partially solved for more than twenty years even in the most basic case of dyadic orthonormal wavelets in a single dimension. These include issues related to the MRA structure (for example, a complete understanding of filters), the structure of the space of negative dilates (in particular, with respect to what is known as the Baggett problem), and the variety of resolution structures that may occur. In this article we offer a comprehensive, yet technically fairly elementary approach to these questions. On this path, we present a multitude of new results, resolve some of the old questions, and provide new advances for some problems that remain open for the future"-- Provided by publisher.

Notes:

Includes bibliographical references.

ISBN:

9781470453749

1470453746

OCLC:

1350632580