Displaying similar documents to “On Analytic Vectors for Unitary Representations of Infinite Dimensional Lie Groups”

Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part

Patrick Bonckaert, Freek Verstringe (2012)

Annales de l’institut Fourier

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We explore the convergence/divergence of the normal form for a singularity of a vector field on ℂ n with nilpotent linear part. We show that a Gevrey- α vector field X with a nilpotent linear part can be reduced to a normal form of Gevrey- 1 + α type with the use of a Gevrey- 1 + α transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small.

Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group

Do Duc Thai, Dinh Huy Hoang (1999)

Annales Polonici Mathematici

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We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection π 1 : V → Γ is finite and proper, then R V : O ( Γ × G ) → I m R V ⊂ O ( V ) has a right inverse

A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform

Bent Ørsted, Jorge Vargas (2007)

Annales de l’institut Fourier

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In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the ( L 2 , L 2 ) -continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is ( L p , L p ) -continuous for 1 ≤ p ≤ ∞ .

A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators

Paulo D. Cordaro, Nicholas Hanges (2009)

Annales de l’institut Fourier

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Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let q be a characteristic point for P . We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that P is analytic hypoelliptic at q . Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained...

Representation of a gauge group as motions of a Hilbert space

Clara Lucía Aldana Domínguez (2004)

Annales mathématiques Blaise Pascal

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This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject. In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered...