Abstract
In this chapter, we present a method of construction of spectral representations of positive definite kernels by the eigenfunctions of operators (theorems of Bochner’s type on positive definite functions, representations of moment sequences, and so on). The main idea of this construction can be explained most simply if we take a positive definite function of a single variable as an example.
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© 1995 Springer Science+Business Media Dordrecht
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Berezansky, Y.M., Kondratiev, Y.G. (1995). Application of the Theory of Expansions to Harmonic Analysis. In: Spectral Methods in Infinite-Dimensional Analysis. Mathematical Physics and Applied Mathematics, vol 12/1-2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0509-5_5
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DOI: https://doi.org/10.1007/978-94-011-0509-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4227-7
Online ISBN: 978-94-011-0509-5
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