Displaying 101 – 120 of 334

Showing per page

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

Nicola Garofalo, Ermanno Lanconelli (1990)

Annales de l'institut Fourier

A recent result of Bahouri shows that continuation from an open set fails in general for solutions of u = V u where V C and = 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 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 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...

Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

Jean Ludwig, Lyudmila Turowska (2006)

Studia Mathematica

Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate...

Currently displaying 101 – 120 of 334