Open AccessIntegral representations of positive definite functions of one variable, associated with operator $\frac{d^4}{dx^4}$
Author(s) -
О. В. Лопотко
Publication year - 2016
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241610
Subject(s) - mathematics , positive definite matrix , operator (biology) , differential operator , variable (mathematics) , order (exchange) , pure mathematics , combinatorics , mathematical analysis , physics , quantum mechanics , eigenvalues and eigenvectors , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
We obtain integral representations for positive definite functions of one variable, when kernels $K(x,y)$ are positive definite. The proof is based on the spectral theory of differential operators of fourth order.