Generalized Appell polynomials and Fueter–Bargmann transforms in the polyanalytic setting

Exponential Transforms and Appell Polynomials.

Laguerre-type exponentials and generalized Appell polynomials

General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. 2000 Mathematics Subject Classification. 33C45, 33C99, 30D05, 33B10.

Expansions of Distributions in Term of Generalized Heat Polynomials and Their Appell Transforms

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certai...

Appell Transformation and Canonical Transforms

The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Four...

Appell Polynomials and Their Relatives

This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...