Wszystkie pola: Gelfand pairs - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On Gelfand pairs associated to transitive groupoids
Autorzy:: Toure, I.
Kangni, K.
Powiązania:: https://bibliotekanauki.pl/articles/952843.pdf
Data publikacji:: 2013
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: transitive groupoids
groupoid representation
Gelfand pairs
Opis:: Let G be a topological locally compact, Hausdorff and second countable groupoid with a Haar system and K a compact subgroupoid of G with a Haar system too. (G,K) is a Gelfand pair if the algebra of bi-K-invariant functions is commutative under convolution. In this paper, we give a characterization of Gelfand pairs associated to transitive groupoids which generalize a well-known result in the groups case. Using this result, we prove that the study of Gelfand pairs associated to transitive groupoids is equivalent to that of Gelfand pairs associated to its isotropy groups.
Źródło:: Opuscula Mathematica; 2013, 33, 4; 751-762
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Spectra for Gelfand pairs associated with the Heisenberg group
Autorzy:: Benson, Chal
Jenkins, Joe
Ratcliff, Gail
Worku, Tefera
Powiązania:: https://bibliotekanauki.pl/articles/966993.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: Let K be a closed Lie subgroup of the unitary group U(n) acting by automorphisms on the (2n+1)-dimensional Heisenberg group $H_n$. We say that $(K,H_n)$ is a Gelfand pair when the set $L^1_K(H_n)$ of integrable K-invariant functions on $H_n$ is an abelian convolution algebra. In this case, the Gelfand space (or spectrum) for $L^1_K(H_n)$ can be identified with the set $Δ(K,H_n)$ of bounded K-spherical functions on $H_n$. In this paper, we study the natural topology on $Δ(K,H_n)$ given by uniform convergence on compact subsets in $H_n$. We show that $Δ(K,H_n)$ is a complete metric space and that the 'type 1' K-spherical functions are dense in $Δ(K,H_n)$. Our main result shows that one can embed $Δ(K,H_n)$ quite explicitly in a Euclidean space by mapping a spherical function to its eigenvalues with respect to a certain finite set of ($K ⋉ H_n$)-invariant differential operators on $H_n$. This viewpoint on the spectrum for $Δ(K,H_n)$ was previously known for K=U(n) and is referred to as 'the Heisenberg fan'.
Źródło:: Colloquium Mathematicum; 1996, 71, 2; 305-328
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

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