Marvin Rosenblum

Generalized Hermite Polynomials and the Bose-Like Oscillator Calculus

This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator calculus, which generalizes the calculus associated with the quantum mechanical simple harmonic oscillator, is studied in terms of these polynomials.

A corona theorem for countably many functions

AbstractSuppose a = {aj}1∞ is a sequence of H∞ functions on the unit disk D such that

An operator-theoretic approach to theorems of the Pick-Nevanlinna and Loewner types. I

||a||_\infty = \mathop {\sup }\limits_{z \in D} (\sum\limits_1^\infty { |a_j (z)|^2 } )^{{\raise0.5ex\hbox{

Restrictions of analytic functions. III

\scriptstyle 1

A plancherel theory for Newton spaces

}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{

Phragmén-Lindelöf Principle

\scriptstyle 2

Some problems of best approximation with constraints

}}}< \infty

Loewner’s Differential Equation

. We show that there exists a sequence c = {cj}∞1 of H∞ functions with ∥c∥∞ < ∞ and satisfying