Titlebook: Spectral Methods in Infinite-Dimensional Analysis; Y. M. Berezansky,Y. G. Kondratiev Book 1995 Springer Science+Business Media Dordrecht 1

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Application of the Theory of Expansions to Harmonic Analysis,rems 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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Infinite-Dimensional Elliptic Differential operators of the Second Order,e used (though often on a formal level) as operators of energy of systems with infinitely many degrees of freedom; in the theory of random processes where diffusion processes with infinite-dimensional phase spaces are constructed with the help of operators of this sort; and, finally, the investigati

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Generalized Functions of Infinitely Many Variables. Gaussian Measures,e of the Lebesgue type is absent in ℝ. and, thus, the choice of a space ..(ℝ.) is ambiguous. Therefore, there is no natural way of identifying an ordinary function with a generalized one, and this yields difficulties.

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Rigged Spaces, (negative) vectors, and the “zero” space .. setting the duality. These constructions are now well known and frequently used. Nevertheless, in Section 1, we give the necessary information with proofs (sometimes concise).

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