The Trotter-Kato product formula for Gibbs semigroups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

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A new product formula involving Bessel functions

Integral Transforms and Special Functions ◽

10.1080/10652469.2021.1926454 ◽

2021 ◽

pp. 1-17

Author(s):

Mohamed Amine Boubatra ◽

Selma Negzaoui ◽

Mohamed Sifi

Keyword(s):

Bessel Functions ◽

New Product ◽

Product Formula

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Completely bounded bimodule maps and spectral synthesis

International Journal of Mathematics ◽

10.1142/s0129167x17500677 ◽

2017 ◽

Vol 28 (10) ◽

pp. 1750067 ◽

Cited By ~ 2

Author(s):

M. Alaghmandan ◽

I. G. Todorov ◽

L. Turowska

Keyword(s):

Tensor Product ◽

Compact Group ◽

Closed Subset ◽

Spectral Synthesis ◽

Locally Compact Group ◽

Product Formula ◽

Fourier Algebra ◽

Locally Compact ◽

Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

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Zero correlation with lower-order terms for automorphic L-functions

International Journal of Number Theory ◽

10.1142/s1793042116500032 ◽

2016 ◽

Vol 12 (01) ◽

pp. 27-55

Author(s):

Timothy L. Gillespie ◽

Yangbo Ye

Keyword(s):

Lower Order ◽

Product Formula ◽

Cuspidal Representation ◽

Zero Correlation ◽

Lower Order Terms ◽

Refined Version ◽

Low Order

Let [Formula: see text] be a self-contragredient automorphic cuspidal representation of [Formula: see text] for [Formula: see text]. Using a refined version of the Selberg orthogonality, we recompute the [Formula: see text]-level correlation of high non-trivial zeros of the product [Formula: see text]. In the process, we are able to extract certain low-order terms which suggest the asymptotics of these statistics are not necessarily universal, but depend upon the conductors of the representations and hence the ramification properties of the local components coming from each [Formula: see text]. The computation of these lower-order terms is unconditional as long as all [Formula: see text].

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