2017
Том 69
№ 7

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Spectral approach to white noise analysis

Berezansky Yu. M., Livinskii V. O., Lytvynov E. V.

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Abstract

By using the spectral projection theorem, we construct the classical Segal transformation as a Fourier transformation in the generalized joint eigenvectors of a certain family of field operators. It is noted that the spectral approach to the Segal transformation, which forms the basis of the analysis of Gaussian white noise, enables one to construct a significant generalization of this transformation.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 3, pp 183-203.

Citation Example: Berezansky Yu. M., Livinskii V. O., Lytvynov E. V. Spectral approach to white noise analysis // Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 177–197.

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