s is a time-frequency transform based on the concept of short-time fourier transform and wavelet transform. the main property of this transform that separate it from the discrete short-time fourier transform is variable frequency resolution. but in this transform the change of resolution of high frequencies to low frequencies is very high. so another transform as a modified s transform is intro...

This paper investigates the S -transform on the space of tempered Boehmians. Inversion and properties are also discussed.

We show that every R–diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu’s S–transform is multiplicative. Our considerations base on a new concept of R–diagonality with amalgamation, for which we give several equivalent characterizat...

Keywords: Quadratic transformation Hypergeometric function of order two Kummer–type transformations Bailey's transform a b s t r a c t By applying various known summation theorems to a general formula based upon Bailey's transform theorem due to Slater, Exton has obtained numerous new quadratic transformations involving hypergeometric functions of two and of higher order. Some of the results ha...

A nonlinear generalization of the S-transform known in Gaussian analysis is introduced. It is deened as a nonlinear operator on topolog-ical spaces of entire functions of innnitely many variables with growth of at most second order and nite type restricted to a certain value. This nonlinear S-transform (NLST) has xed points a certain family of which is found and analyzed. In particular, their s...

We introduce the operator Z that is often called the Zak transform. Our definition is a bit different from the one that usually appears in the literature. We will discuss this difference and will also give a historical account that the reader may find particularly interesting. In order to do this, however, we need to present our treatment of the operator Z (and Z̃) which shows that the Fourier t...