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A recent result of Bahouri shows that continuation from an open set fails in general for solutions of $ℒ u = V u$ where $V \in C^{\infty}$ and $ℒ = \sum_{j = 1}^{N - 1} X_{j}^{2}$ is a (nonelliptic) operator in $R^{N}$ satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when $ℒ$ is the subelliptic Laplacian on the Heisenberg group and $V$ is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of $ℒ u = V u$ to have a finite order...

Front d'onde et propagation des singularités pour un vecteur-distribution

Dominique Manchon (1999)

Colloquium Mathematicae

We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Khalid Koufany, Bent Ørsted (1996)

Annales de l'institut Fourier

For the scalar holomorphic discrete series representations of $SU (2, 2)$ and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside $SU (2, 2)$ . We construct a Cayley transform between the Ol’shanskiĭ semigroup having $U (1, 1)$ as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for $SU (2, 2)$ . This allows calculating the composition series in terms of harmonic analysis on $U (1, 1)$ . In particular we show that the Ol’shanskiĭ Hardy space for $U (1, 1)$ is different...

Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms

Ewa Damek (1997)

Colloquium Mathematicae

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Fonctions harmoniques positives sur certains groupes de Lie résolubles connexes

Fonctions indéfiniment différentiables invariantes sur l'espace tangent d'un espace symétrique

Formule de Plancherel pour GL (n, C) / U (p, q).

Formules d'inversion pour des intégrales orbitales.

Fourier and Poisson transformation associated to a semisimple Symmetrie space.

Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

Front d'onde et propagation des singularités pour un vecteur-distribution

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Functional calculus of Lie groups and wave propagation.

Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups

Fundamental solutions for translation and rotation invariant differential operators on the Heisenberg group

Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms

Currently displaying 1 – 12 of 12