Uncertainty principles for the windowed Hankel transform

Paley-Wiener Theorems and Uncertainty Principles for the Windowed Linear Canonical Transform

In a recent paper the authors have introduced the windowed linear canonical transform and shown its good properties together with some applications such as Poisson summation formulas, sampling interpolation and series expansion. In this paper we prove the Paley-Wiener theorems and the uncertainty principles for the (inverse) windowed linear canonical transform. They are new in literature and ha...

The Hankel transform

Hermite Functions and Uncertainty Principles for the Fourier and the Windowed Fourier Transforms

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on R which may be written as P (x) exp(Ax, x), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f̂(y). We also give the best constant in uncertainty principles of Gelf’and Shilov type. We then obtain sim...

Matlab code for the Discrete Hankel Transform

Transformations Preserving the Hankel Transform

Transformations Preserving the Hankel Transform Christopher French Department of Mathematics and Statistics Grinnell College Grinnell, IA 50112 USA [email protected] Abstract We classify all polynomial transformations of integer sequences which preserve the Hankel transform, thus generalizing examples due to Layman and Spivey & Steil. We also show that such transformations form a group ...