On Calculating Response Functions Via Their Lorentz Integral Transforms

On Q-integral Transforms and Their Applications

In this paper, we introduce a q-analogue of the P-Widder transform and give a Parseval-Goldstein type theorem. Furthermore, we evaluate the q-Laplace transform of a product of q-Bessel functions. Several special cases of our results are also pointed out.

Supports of Functions and Integral Transforms

In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...

Integral Transforms of Functions with Restricted Derivatives

Generalizations of the Fractional Calculus, Special Functions and Integral Transforms and Their Relationships

In this survey talk we aim to clarify the close relationships between the operators of the generalized fractional calculus (GFC), some classes of generalized hypergeo-metric functions and generalizations of the classical integral transforms. The GFC developed in [1] is based on the essential use of the Special Functions (SF). The generalized (multiple) fractional integrals and derivatives are d...

Linearized path integral approach for calculating nonadiabatic time correlation functions.

We show that quantum time correlation functions including electronically nonadiabatic effects can be computed by using an approach in which their path integral expression is linearized in the difference between forward and backward nuclear paths while the electronic component of the amplitude, represented in the mapping formulation, can be computed exactly, leading to classical-like equations o...