ON OPERATOR-PARAMETER TRANSFORMS BASED ON NUCLEAR ALGEBRA OF ENTIRE FUNCTIONS AND APPLICATIONS

摘要

Based on nuclear algebra of entire functions, we extend some results about operatorparameter transforms involving the Fourier-Gauss and Fourier-Mehler transforms. We investigate the solution of a initial-value problem associated to infinitesimal generators of these transformations. In particular, by using convolution product,we show to what extent regularity properties can be performed on our setting.