Mathematics, Informatics, Physics: Science and Education

Electronic scientific journal

Vol. 3 No. 1 (2026)
ARTICLES

A Class of Positive Definite Kernels with Cubic Symmetrization

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  • Ivanna Andrusyak,
  • Oksana Brodyak
Ivanna Andrusyak
Lviv Polytechnic National University
Bio
Oksana Brodyak
Lviv Polytechnic National University
Bio

Published 2026-05-27

Keywords

  • integral representation,
  • kernels,
  • positive definite function

Copyright (c) 2026 Іванна Андрусяк, Оксана Бродяк

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A Class of Positive Definite Kernels with Cubic Symmetrization. (2026). Mathematics, Informatics, Physics: Science and Education, 3(1), 1-10. https://doi.org/10.31652/3041-1955-2026-03-01-01
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Abstract

The class of positive definite kernels K(x,y) generated by an entire function k by means of symmetrization associated with cube roots of unity is investigated. For kernels consistent with the spectral structure of the third-order problem u'''=λu, an explicit integral representation of the function k in terms of a nonnegative spectral measure dρ(λ) with compact support is obtained. The obtained formula determines the constructive parameterization of admissible kernels in the considered class and establishes a direct connection between positive definiteness and spectral data.

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