Spectral approach to white noise analysis

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.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 177–197, March, 1994.This research was supported by the Ukrainian State Committee on Science and Technology and by the Swiss National Foundation (SNF).