Cite this article as:

Garkovskaya S. . Nonseparable Wavelets of Meyer Type in Besov and Lizorkin – – Triebel Spaces. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2009, vol. 9, iss. 2, pp. 12-18. DOI: https://doi.org/10.18500/1816-9791-2009-9-2-12-18

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.5

Nonseparable Wavelets of Meyer Type in Besov and Lizorkin – – Triebel Spaces

Authors: 
Garkovskaya S.A. , Voronezh State University, Russia, 394006, Voronezh, Universitetskaya pl., 1 , GarkovskayaSA@mail.ru
Abstract: 

Iti sproved that Fourier transforms of nonseparable wavelets of Meyer type can be used as decomposition of unity in definition of Besov and Lizorkin – Triebel spaces. The result is the first step in the proof of unconditional basisness of above mentioned wavelets in scales under consideration.

Key words: 
wavelet, nonseparable wavelets, Besov spaces, Lizorkin – Triebel spaces, decomposition of unity
DOI: 
https://doi.org/10.18500/1816-9791-2009-9-2-12-18
References

1. Новиков И.Я., Протасов В.Ю., Скопина М.А. Теория всплесков. М.: Физматлит, 2005. 616 с.

2. Bownik M., Speegle D. Meyer Type Wavelet Bases in R2 // J. of Approx. Theory. 2002. V. 116. P. 49–75.

3. Lindemann M. Approximation Properties of Non
Separable Wavelet Bases with Isotropic Scaling Matrices and their Relations to Besov Spaces / University Bremen. Bremen, 2005. 126 p.

4. Трибель Х. Теория функциональных пространств. М.: Мир, 1986. 448 с.
 

Full text:
download
63