Geodesic
Spline-wavelet decomposition on an interval
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 107-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the second-order spline-wavelet representations on an interval, the conditions under which decomposition operators are independent of the order of elementary operations are established. The notion of $k$-localized systems of functionals is introduced, and the operator set in which the embedding operator possesses a unique left inverse is studied. 
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Yu. K. Dem'yanovich; B. G. Vager. Spline-wavelet decomposition on an interval. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 107-131. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a7/

[1] Yu. K. Demyanovich, O. M. Kosogorov, “Kalibrovochnye sootnosheniya dlya nepolinomialnykh splainov”, Probl. matem. analiza, 43, 2009, 3–19

[2] Yu. K. Demyanovich, “Negladkie splain-veivletnye razlozheniya i ikh svoistva”, Zap. nauchn. semin. POMI, 395, 2012, 31–60 | MR | Zbl

[3] Yu. K. Demyanovich, Teoriya splain-vspleskov, SPb., 2013, 526 pp.