2 4 A ug 1 99 7 Symbolic calculus on the time - frequency half - plane

2 8 N ov 1 99 7 Symbolic calculus on the time - frequency half - plane

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f > 0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the assoc...

Symbolic calculus on the time-frequency half-plane

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f > 0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the assoc...

ar X iv : h ep - t h / 99 05 22 4 v 2 2 7 A ug 1 99 9 Whitham Deformations and Tau Functions in N = 2 Supersymmetric Gauge Theories ∗

We review new aspects of integrable systems discovered recently in N = 2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten curves for classical gauge groups, (ii) its application to contact terms in the u-plane integral of topologically twisted theories, and (iii) a connection be...

4 v 1 2 A ug 1 99 7 RESULTS ON DIFFRACTION

2 4 A ug 1 99 9 Umbral presentations for polynomial sequences

Using random variables as motivation, this paper presents an exposition of formalisms developed in [RT1, RT2] for the classical umbral calculus. A variety of examples are presented, culminating in several descriptions of sequences of binomial type in terms of umbral polynomials.