✦ LIBER ✦
An Inequality for Fourier–Laplace Transforms of Entire Functions, and the Existence of Exponential Frames in Fock Space
✍ Scribed by Bo Berndtsson
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 318 KB
- Volume
- 149
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
We study mapping properties of the Fourier Laplace transform between certain spaces of entire functions. We introduce a variant of the classical Fock space by integrating against the Monge AmpeÁ re measure of the weight function and show that the norm of the Fourier Laplace transform, in a dual Fock space, dominates the norm of the function. Equality holds when the weight function is an Hermitean form. As an application we get a criterium for the existence of frames of exponential functions in Fock space.