(q,μ) and (p,q,ζ)-exponential functions: Rogers–Szegő polynomials and Fourier–Gauss transform

Constructible exponential functions, motivic Fourier transform and transfer principle

We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative settings. This allows us to define a motivic Fourier transformation for which we get various inversion statements. We also define spaces of motivic Schwartz-Bruhat functions on which motivic Fourier transformation induces isomorphisms. Our m...

Generalized Exponential Euler Polynomials and Exponential Splines

Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.

Bernstein's polynomials for convex functions and related results

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

Exponential polynomials and D-modules

We introduce D-modules adapted to study ideals generated by exponential polynomials. ∗Partially supported by the NSF grants DMS-9000619 and CDR-8803012 †Partially supported by the NSF grant DMS-9000619

Exponential Transforms and Appell Polynomials.