Variations on uncertainty principles for integral operators

Abstract

The aim of this paper is to prove new uncertainty principles for an integral operator with a bounded kernel. To do so we prove a Nash-type inequality and a Carlson-type inequality for this transformation. From this we deduce a variation on Heisenberg’s uncertainty inequality and Faris’s local uncertainty principle. We also prove a variation on Donoho-Stark’s uncertainty principle. Our results can be applied to a wide variety of integral operators, including the Fourier transform, the Fourier-Bessel transform, the generalized Fourier transform and the-transform.

Keywords:

• integral operators
• G-transform
• generalized Fourier transform
• uncertainty principles

AMS Subject Classifications:

• 42A68
• 42C20