Naslov
One-Dimensional Dyadic Wavelets

Autori
Luthy, Peter ; Šikić, Hrvoje ; Soria, Fernando ; Weiss, Guido ; Wilson, Edward

Izvornik
Memoirs of the American Mathematical Society (0065-9266) 280 (2022), 1378; 1-152

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Wavelets ; Shift invariant spaces ; Low pass filters ; MRA

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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