A Class of Positive Definite Kernels with Cubic Symmetrization
DOI:
https://doi.org/10.31652/3041-1955-2026-03-01-01Keywords:
integral representation, kernels, positive definite functionAbstract
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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