For spline-wavelet representations of the second-order on an interval, 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. Bibliography: 3 titles.
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Yu. K. Dem’yanovich and O. M. Kosogorov, “Calibration relations for nonpolynomial splines,” Probl. Matem. Anal., 43, 3–19 (2009).
Yu. K. Dem’yanovich, “Nonsmooth spline-wavelet expansions and their properties,” Zap. Nauchn. Semin. POMI, 395, 31–60 (2012).
Yu. K. Dem’yanovich, The Theory of Spline - Wavelets [in Russian], SPbGU, St. Petersburg (2013).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 428, 2014, pp. 107–131.
This work was supported by the Russian Foundation for Basic Research (projects Nos. 15- 01-08847 and 13-01-00096.)
Translated by Yu. K. Dem’yanovich and B. G. Vager.
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Dem’yanovich, Y.K., Vager, B.G. Spline-Wavelet Decomposition on an Interval. J Math Sci 207, 736–752 (2015). https://doi.org/10.1007/s10958-015-2396-3
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DOI: https://doi.org/10.1007/s10958-015-2396-3