Complex Hermite functions as Fourier–Wigner transform

The bilinear Hilbert transform acting on Hermite and Laguerre functions

We obtain several formulas for the action of the bilinear Hilbert transform on pairs of Hermite and Laguerre functions. The result can be expressed as a linear combination of products of Hermite or Laguerre functions.

A fast Hermite transform

We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Trade-offs between approximation in bandlimit (in the Hermite sense) and size of the support region are addressed. Numerical experiments are prese...

Hermite functions

We define S to be the set of those φ ∈ C∞(R,C) such that pn(φ) < ∞ for all n ≥ 0. S is a complex vector space and each pn is a norm, and because each pn is a norm, a fortiori {pn : n ≥ 0} is a separating family of seminorms. With the topology induced by this family of seminorms, S is a Fréchet space. As well, D : S → S defined by (Dφ)(x) = φ′(x), x ∈ R 1http://individual.utoronto.ca/jordanbell/...

Schwartz functions, Hermite functions, and the Hermite operator

On Hermite-tricomi Functions of the Single Complex Variable

In this paper, we define a new kind of the hypergeometric function, say, Hermite-Tricomi functions. An explicit representation, recurrence relations for the Hermite-Tricomi functions are given and differential equations satisfied them is presented. A new expansions of the exponential for a wide class of functions, whose properties, including recurrences, addition theorems, generating functions ...