Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functional calculus for a bounded $C_0$-semigroup on Hilbert space   We introduce a new Banach algebra ${\mathcal A}({\mathbb C}_+)$ of bounded
analytic functions on ${\mathbb C}_+=\{z\in{\mathbb C}\, :\, {\rm Re}(z)>0\}$
which is an analytic version of the Figa-Talamenca-Herz algebras on ${\mathbb
R}$. Then we prove that the negative generator $A$ of any bounded
$C_0$-semigroup on Hilbert space $H$ admits a bounded (natural) functional
calculus $\rho_A\colon {\mathcal A}({\mathbb C}_+)\to B(H)$. We prove that this
is an improvement of the bounded functional calculus ${\mathcal B}({\mathbb
C}_+)\to B(H)$ recently devised by Batty-Gomilko-Tomilov on a certain Besov
algebra ${\mathcal B}({\mathbb C}_+)$ of analytic functions on ${\mathbb C}_+$,
by showing that ${\mathcal B}({\mathbb C}_+)\subset {\mathcal A}({\mathbb
C}_+)$ and ${\mathcal B}({\mathbb C}_+)\not= {\mathcal A}({\mathbb C}_+)$. In
the Banach space setting, we give similar results for negative generators of
$\gamma$-bounded $C_0$-semigroups. The study of ${\mathcal A}({\mathbb C}_+)$
requires to deal with Fourier multipliers on the Hardy space $H^1({\mathbb
R})\subset L^1({\mathbb R})$ and we establish new results on this topic.

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The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph