Integral representations of positive definite functions of one variable, associated with operator $$$\frac{d^4}{dx^4}$$$
Abstract
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.
Keywords
integral representation; positive definite functions
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Krejn M.G. "On one general method of expansion of positive definite kernels into elementary products", Doklady AN sssr, 1946; 53(1): pp. 3-6.
Lopotko O.V. "Integral representation of positive definite functions of one variable, associated with operator $$$\frac{d^3}{dx^3}$$$", Visnyk ONU, 2013; 18(4(20)): pp. 31-38.
DOI: https://doi.org/10.15421/241610
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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
