Fourier Transform of Nilpotently Supported Invariant Functions on a Simple Lie Algebra over a Finite Field.
Fourier transform of Schwartz functions on the Heisenberg group
Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.
Fourier transformation and endoscopy. (Transformation de Fourier et endoscopie.)
Fourier transforms of representations of quaternions.
Fourier-like kernels in geometric quantization [Book]
Fourier-Stieltjes algebras of compact extensions of nilpotent groups.
Free fall motion in an invariant field of forces: the 2D-case.
Free groups of semigroups in semi-simple Lie groups.
Free products of Lie groups
Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation
A recent result of Bahouri shows that continuation from an open set fails in general for solutions of where and is a (nonelliptic) operator in satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when is the subelliptic Laplacian on the Heisenberg group and 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 to have a finite order...
From a topological theory of semigroup to a geometric one.
Front d'onde et propagation des singularités pour un vecteur-distribution
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
For the scalar holomorphic discrete series representations of and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside . We construct a Cayley transform between the Ol’shanskiĭ semigroup having as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for . This allows calculating the composition series in terms of harmonic analysis on . In particular we show that the Ol’shanskiĭ Hardy space for is different...
Functional calculus of Lie groups and wave propagation.
Functional equation satisfied by certain -functions
Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups
Functions on the universal cover of the prinicpal nilpotent orbit.
Functorial prolongations of Lie groups and their actions
Functoriality and the Inverse Galois problem II: groups of type and
This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control...
Functoriality for the classical groups