Displaying similar documents to “Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program”

A note on Howe's oscillator semigroup

Joachim Hilgert (1989)

Annales de l'institut Fourier

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Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the L 2 ( ℝ n ) and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.

Restricting cuspidal representations of the group of automorphisms of a homogeneous tree

Donald I. Cartwright, Gabriella Kuhn (2003)

Bollettino dell'Unione Matematica Italiana

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Let X be a homogeneous tree in which every vertex lies on q + 1 edges, where q ≥ 2 . Let A = A ⁢ u ⁢ t ⁢ X be the group of automorphisms of X , and let H be the its subgroup P ⁢ G ⁢ L ⁢ 2 , F , where F is a local field whose residual field has order q . We consider the restriction to H of a continuous irreducible unitary representation π of A . When π is spherical or special, it was well known that π remains irreducible, but we show that when π is cuspidal, the situation is much more complicated. We then study in detail what happens...

Generalization of Fueter's result to R n + 1

Tao Qian (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Fueter's result (see [6,8]) on inducing quaternionic regular functions from holomorphic functions of a complex variable is extended to Euclidean spaces R n + 1 . It is then proved to be consistent with M. Sce's generalization for n being odd integers [6].

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

Jean-Pierre Ramis, Yasutaka Sibuya (1994)

Annales de l'institut Fourier

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We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation x d y → d x = G → 0 ( x ) + λ ( x ) + A 0 y → + x μ G → ( x , y → ) , the idea of our proof is to interpret...