Naslov
Wavelets and MRA Filters

Autori
Šikić, Hrvoje

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
7th Croatian Mathematical Congress / Ćurković, Andrijana - Split : Mathematical Society : University of Split, Faculty of Science, 2022, 1-2

ISBN
978-953-7155-24-7

Skup
7th Croatian Mathematical Congress

Mjesto i datum
Split, Hrvatska, 15.06.2022. - 18.06.2022

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Wavelets ; MRA Filters

Sažetak
We will present some results from the newly developed theory of wavelets ; based on the joint work with the following authors: [1] P.M.Luthy, H.Šikić, F.Soria, G.L.Weiss, E.N.Wilson. One-Dimensional Dyadic Wavelets. To appear in the Memoir of the AMS, vii + 152 pages. For the last three decades the research of our group has been highly influenced by the connection between wavelets and Fourier analysis as outlined in the influential book by E.Hernandez and G.Weiss. The approach was to study wavelets and other reproducing function systems via the four basic equations that characterized various properties of wavelet systems, like frame and basis properties, completeness, orthogonality, etc. Despite hundreds of research papers and the impressive development of the theory of such systems, some questions remain open even in the basic case of dyadic wavelets on the real line. In [1] we address several of these questions. Among the most thourough treatments that we provide in this lengthy paper is the issue of the understanding of the low-pass filters associated with the MRA structure. In this talk we will focus on some of these results. As it turned out, a more general and abstract approach to the problem, using the study of dyadic orbits and newly introduced Tauberian function, reveals several interesting properties and opens an interesting context for some older results. We shall compare our reults with older results achieved by Cohen, Lawton, Gundy, and many others, including some members of our group. Guido Weiss, who recently passed away, was the plenary lecturer for the Third Croatian Math Congress, also in Split ; it was the first congress held outside of Zagreb, and as such of a particular importance for the future of Croatian mathematical congresses.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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