Year: 2014
Type: preprint
Abstract: We study dilated holomorphic $L^p$ space of Gaussian measures over $\mathbb{C}^n$, denoted $\mathcal{H}_{p,α}^n$ with variance scaling parameter $α>0$. The duality relations $(\mathcal{H}_{p,α}^n)^\ast \cong \mathcal{H}_{p',α}$ hold with $\frac{1}{p}+\frac{1}{p'}=1$, but not isometrically. We identify the sharp lower constant comparing the norms on $\mathcal{H}_{p',α}$ and $(\mathcal{H}_{p,α}^n)^\ast$, and provide upper and lower bounds on the sharp upper constant. We prove several suggestive partial results on the sharpness of the upper constant. One of these partial results leads to a sharp bound on each Taylor coefficient of a function in the Fock space for $n=1$.
Source: arXiv (Cornell University)
Authors: Gryc, William E., Kemp, Todd
Institutions: Muhlenberg College, University of California San Diego
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2019577061