Geodesic
Local wavelet basis for an irregular grid
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 84-110

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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},
     publisher = {mathdoc},
     volume = {334},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a6/}
}
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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/