Geodesic
Discrete periodic multiresolution analysis
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 7-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Discrete periodic multiresolution analysis. Multiresolution analyses in the space of discrete periodic complex-valued functions are studied. Characterization of a multiresolution analysis in terms of Fourier coefficients of functions that form a corresponding scaling sequence is obtained. An example of a multiresolution analysis with scaling sequence that consists of trigonometric polynomials with minimally supported spectrum is provided. 
@article{ZNSL_2021_499_a1,
     author = {P. A. Andrianov},
     title = {Discrete periodic multiresolution analysis},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--21},
     year = {2021},
     volume = {499},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a1/}
}
TY  - JOUR
AU  - P. A. Andrianov
TI  - Discrete periodic multiresolution analysis
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 7
EP  - 21
VL  - 499
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a1/
LA  - ru
ID  - ZNSL_2021_499_a1
ER  - 
%0 Journal Article
%A P. A. Andrianov
%T Discrete periodic multiresolution analysis
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 7-21
%V 499
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a1/
%G ru
%F ZNSL_2021_499_a1
P. A. Andrianov. Discrete periodic multiresolution analysis. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part I, Tome 499 (2021), pp. 7-21. http://geodesic.mathdoc.fr/item/ZNSL_2021_499_a1/

[1] B. Han, “On dual wavelet tight frames”, ACHA, 4 (1997), 380–413 | Zbl

[2] B. Han, “Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix”, J. Comput. Appl. Math., 155 (2003), 43–67 | DOI | MR | Zbl

[3] A. Ron, Z. Shen, “Gramian analysis of affine bases and affine frames”, Approximation Theory VIII, v. 2, Wavelets, eds. C.K. Chui, L. Schumaker, World Scientific, Publishing Co. Inc, Singapore, 1995, 375–382 | Zbl

[4] A. Ron, Z. Shen, “Frame and stable bases for shift-invariant subspaces of L2(Rd)”, Canad. J. Math., 47:5 (1995), 1051–1094 | DOI | MR | Zbl

[5] A. Krivoshein, V. Protasov, M. Skopina, Multivariate Wavelet Frames, Springer, Singapore, 2016 | Zbl

[6] C. K. Chui, J. Z. Wang, “A general framework of compact supported splines and wavelets”, J. Approx. Theory, 71 (1992), 263–304 | DOI | MR | Zbl

[7] S. S. Gon, S. Z. Lee, Z. Shen, W. S. Tang, “Construction of Schauder decomposition on banach spaces of periodic functions”, Proceedings of the Edinburgh Mathematical Society, 41:1 (1998), 61–91 | DOI | MR

[8] A. P. Petukhov, “Periodic wavelets”, Mat. Sb., 188:10 (1997), 69–94 | DOI | MR | Zbl

[9] V. A. Zheludev, “Periodic splines and wavelets”, Proc. of the Conference “Math. Analysis and Signal Processing” (Cairo, Jan. 2–9, 1994)

[10] M. Skopina, “Multiresolution analysis of periodic functions”, East Journal on Approximations, 3:2 (1997), 203–224 | MR | Zbl

[11] J. A. Gubner, W.-B. Chang, “Wavelet transforms for discrete-time periodic signals”, Signal Processing, 42 (1995), 167–180 | DOI | Zbl

[12] V. A. Kirushev, V. N. Malozemov, A. B. Pevnyi, “Wavelet Decomposition of the Space of Discrete Periodic Splines”, Mathematical Notes, 67:5 (2000), 603–610 | DOI | MR | Zbl

[13] A. P. Petukhov, “Periodic discrete wavelets”, Algebra i Analiz, 8:3 (1996), 151–183

[14] M. A. Skopina, “Local convergence of Fourier series with respect to periodized wavelets”, J. Approxim. Theory, 94:2 (1998), 191–202 | DOI | MR | Zbl