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On Maximally Oscillating Perfect Splines and Some of Their Extremal Properties

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Abstract

In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using these splines, we characterize the modulus of continuity of the differential operator.

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Acknowledgement

The author would like to thank the referees for their valuable remarks and suggestions.

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  1. Department of Mathematics and Mechanics Oles Honchar Dnipro National University, Gagarina ave. 72, Dnipro, 49010, Ukraine

    O. Kovalenko

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  1. O. Kovalenko
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Correspondence to O. Kovalenko.

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Kovalenko, O. On Maximally Oscillating Perfect Splines and Some of Their Extremal Properties. Anal Math 46, 555–577 (2020). https://doi.org/10.1007/s10476-020-0037-7

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  • DOI: https://doi.org/10.1007/s10476-020-0037-7

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