Energy Moments in Time and Frequency for Two-Scale Difference Equation Solutions and Wavelets

Autor:	Lars F. Villemoes
Rok vydání:	1992
Předmět:	Sobolev space Computational Mathematics Matrix (mathematics) Wavelet Differential equation Spectral radius Applied Mathematics Frequency domain Mathematical analysis Functional equation Analysis Energy (signal processing) Mathematics
Zdroj:	SIAM Journal on Mathematical Analysis. 23:1519-1543
ISSN:	1095-7154 0036-1410
DOI:	10.1137/0523085
Popis:	This paper indicates how to find energy moments in direct and Fourier space of a solution to the functional equation $u(x) = \sum_{k = 0}^{N - 1} {2c_k u(2x - k)} $ and shows that the Sobolev regularity of u is determined by the spectral radius of a matrix defined from the coefficients $(c_k )$. The results are applied to compactly supported orthonormal wavelets.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0ebdc6cb7eeb9a304c3966fd7bb8412d https://doi.org/10.1137/0523085 Zobrazit plný text záznamu