Geodesic
Wavelet decompositions on a manifold
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 26-38 
Yu. K. Dem'yanovich; A. V. Zimin. Wavelet decompositions on a manifold. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 26-38. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a2/
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}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A general method for constructing chains of embedded spline spaces on a smooth (not necessarily compact) manifold is suggested. A wavelet decomposition is obtained for the case of an arbitrary vector space. The results are illustrated by constructing a wavelet decompositon of a chain of embedded spaces of $B_\varphi$-splines of zero order on a smooth manifold.

[1] Yu. K. Demyanovich, Lokalnaya approksimatsiya na mnogoobrazii i minimalnye splainy, SPb., 1994 | MR

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

[3] I. Ya. Novikov, V. Yu. Protasov, M. A. Skopina, Teoriya vspleskov, M., 2005 | MR

[4] J. Maes, A. Bultheel, “Stability analysis of biorthogonal multiwavelets whose duals are not in $L2$ and its application to local semiorthogonal lifting”, Applied Numerical Mathematics, 2007 (to appear) | MR

[5] Yu. K. Demyanovich, “Gladkost prostranstv splainov i vspleskovye razlozheniya”, Doklady RAN, 401:4 (2005), 439–442 | MR

[6] Yu. K. Demyanovich, “Vlozhennost i vspleskovye predstavleniya prostranstv minimalnykh splainov”, Probl. matem. analiza, 35, 2007, 13–41