Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Sharp Constants for Dual Segal--Bargmann $L^p$ Spaces   We study dilated holomorphic $L^p$ space of Gaussian measures over
$\mathbb{C}^n$, denoted $\mathcal{H}_{p,\alpha}^n$ with variance scaling
parameter $\alpha>0$. The duality relations $(\mathcal{H}_{p,\alpha}^n)^\ast
\cong \mathcal{H}_{p',\alpha}$ hold with $\frac{1}{p}+\frac{1}{p'}=1$, but not
isometrically. We identify the sharp lower constant comparing the norms on
$\mathcal{H}_{p',\alpha}$ and $(\mathcal{H}_{p,\alpha}^n)^\ast$, 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 $n=1$.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph