Geodesic
Local wavelet basis for an irregular grid
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 84-110 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The spaces of $\mathcal B_\varphi$-splines are proved to be embedded for an arbitrary grid refinement; the direct (wavelet) decomposition for chains of embedded spaces of $\mathcal B_\varphi$-splines on a sequence of refined irregular grids is discussed; a wavelet basis of functions with compact supports is constructed; formulas of decomposition and reconstruction are provided. Simple solutions of certain interpolation problems in the spaces considered are suggested. Examples of the spline spaces are presented. 
@article{ZNSL_2006_334_a6,
     author = {Yu. K. Dem'yanovich},
     title = {Local wavelet basis for an irregular grid},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {84--110},
     year = {2006},
     volume = {334},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a6/}
}
TY  - JOUR
AU  - Yu. K. Dem'yanovich
TI  - Local wavelet basis for an irregular grid
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 84
EP  - 110
VL  - 334
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a6/
LA  - ru
ID  - ZNSL_2006_334_a6
ER  - 
%0 Journal Article
%A Yu. K. Dem'yanovich
%T Local wavelet basis for an irregular grid
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 84-110
%V 334
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a6/
%G ru
%F ZNSL_2006_334_a6
Yu. K. Dem'yanovich. Local wavelet basis for an irregular grid. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 84-110. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a6/

[1] M. D. Buhmann, “Multiquadratic prewavelets on nonequally spaced knots in one dimension”, Math. Comput., 64 (1995), 1611–1625 | DOI | MR | Zbl

[2] I. Ya. Novikov, S. B. Stechkin, “Osnovy teorii vspleskov”, Uspekhi mat. nauk, 53 (1998), 53–128 | MR | Zbl

[3] S. Malla, Veivlety v obrabotke signalov, Mir, M., 2005

[4] Yu. K. Demyanovich, “O vlozhennosti prostranstv minimalnykh splainov”, Zh. vychisl. matem. matem. fiz., 40 (2000), 1012–1029 | MR

[5] I. G. Burova, Yu. K. Demyanovich, “O splainakh maksimalnoi gladkosti”, Vestnik Sankt-Peterb. univ. Ser. 1, 2004, no. 4, 3–11 | MR

[6] Yu. K. Demyanovich, “Vlozhennye prostranstva trigonometricheskikh splainov i ikh vspleskovoe razlozhenie”, Matem. zametki, 78:5 (2005), 658–675 | MR