Spline-Wavelet Decomposition on an Interval

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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References

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    Yu. K. Dem’yanovich and O. M. Kosogorov, “Calibration relations for nonpolynomial splines,” Probl. Matem. Anal., 43, 3–19 (2009).

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    Yu. K. Dem’yanovich, “Nonsmooth spline-wavelet expansions and their properties,” Zap. Nauchn. Semin. POMI, 395, 31–60 (2012).

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    Yu. K. Dem’yanovich, The Theory of Spline - Wavelets [in Russian], SPbGU, St. Petersburg (2013).

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Correspondence to Yu. K. Dem’yanovich.

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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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Keywords

  • Column Vector
  • Coarsened Grid
  • Linear Independence
  • Elementary Operation
  • Spline Space