We present a new method of calculating intertwining operators between principal series representations of semisimple Lie groups G. Working in the compact realization we find the eigenvalues of the operators on the K-types, and give several examples. Among the advantages of our method is its applicability to bundlevalued cases.1996 Academic Press, Inc.
The Fourier coefficients of a smooth K-invariant function on a compact symmetric space M = U/K are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we describe the size of the support by means of the exponential type of a holomorphic extension of the Fourier coefficients.
In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gröchenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of SL 2 (R).We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation.
In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gröchenig in the 1980's. Spaces that can be described by this new technique include the whole Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we show that atomic decompositions can be constructed through sampling.We further present a wavelet characterization of Besov spaces on the forward light cone.
This paper defines π-weighted Laplace transforms on the spaces of π-covariant functions. By the inverse Laplace transform we define operator-valued Bessel functions. We also study the holomorphic discrete series of the automorphism group of a Siegel domain of type II.
If G is a Lie group, H ⊂ G is a closed subgroup, and τ is a unitary representation of H, then the authors give a sufficient condition on ξ ∈ ig * to be in the wave front set of Ind G H τ . In the special case where τ is the trivial representation, this result was conjectured by Howe. If G is a real, reductive algebraic group and π is a unitary representation of G that is weakly contained in the regular representation, then the authors give a geometric description of WF(π) in terms of the direct integral decomposition of π into irreducibles. Special cases of this result were previously obtained by Kashiwara-Vergne, Howe, and Rossmann. The authors give applications to harmonic analysis problems and branching problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.