Norm of the Hermite-Fejér interpolative operator with derivatives of variable order

  • Alexander Fedotov Department of Physics and Mathematics, Kazan National Research Technical University, 420111 Kazan, Russian Federation
Ariticle ID: 87
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Keywords: variable order derivative, Hermite-Fejér interpolation, Sobolev space, norm estimation

Abstract

A new definition of a variable order derivative is given. It is based on interpolation of integer order differentiation operators. An interpolation operator of the Hermite-Fejér type is built to jointly interpolate the function and its derivative of variable order. The upper estimate of the norm of this operator is obtained. This norm has been shown to be limited.

References

[1] Fedotov AI. Substantiation of a quadrature-difference method for solving integro-differential equations with derivatives of variable order. Computational Mathematics and Mathematical Physics 2022; 62(4): 548–563. doi: 10.1134/S0965542522040066

[2] Fedotov AI. Estimate of the norm of the Hermite-Fejér interpolation operator in Sobolev spaces. Mathematical Notes 2019; 105(6): 905–916. doi: 10.1134/S0001434619050286

[3] Taylor ME. Pseudodifferential Operators (PMS-34). Princeton University Press; 1981.

Published
2023-07-06
How to Cite
Fedotov, A. (2023). Norm of the Hermite-Fejér interpolative operator with derivatives of variable order. Journal of AppliedMath, 1(2), 87. https://doi.org/10.59400/jam.v2i1.87
Section
Article