We obtain an integral representation of even functions of two variables for which the kernel [k 1(x + y) + k 2(x − y)], x, y ∈ R 2, is positive definite.
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Yu. M. Berezans’kyi, “A generalization of the Bochner theorem on expansion in eigenfunctions of differential operators,” Dokl. Akad. Nauk SSSR, 108, No. 3, 893–896 (1956).
Yu. M. Berezans’kyi, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
M. G. Krein, “On one general method for the factorization of positive-definite kernels in elementary products,” Dokl. Akad. Nauk SSSR, 53, No. 1, 3–6 (1946).
O. V. Lopotko, “Integral representation of even positive-definite functions of one variable,” Ukr. Mat. Zh., 62, No. 2, 281–284 (2010); English translation: Ukr. Math. J., 62, No. 2, 320–324 (2010).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 6, pp. 844–853, June, 2011.
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Lopotko, O.V. Integral representation of even positive-definite functions of two variables. Ukr Math J 63, 981–992 (2011). https://doi.org/10.1007/s11253-011-0558-0
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DOI: https://doi.org/10.1007/s11253-011-0558-0