An analogue in commutative harmonic analysis of the uniform bounded approximation property of Banach space
An analogue of Gutzmer's formula for Hermite expansions
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.
An analogue of Hardy's theorem for the Heisenberg group
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.
An application of Grothendieck's inequality to a problem in harmonic analysis
An Application of Littlewood-Paley Theory in Harmonie Analysis.
An application of shift operators to ordered symmetric spaces
We study the action of elementary shift operators on spherical functions on ordered symmetric spaces of Cayley type, where denotes the multiplicity of the short roots and the rank of the symmetric space. For even we apply this to prove a Paley-Wiener theorem for the spherical Laplace transform defined on by a reduction to the rank 1 case. Finally we generalize our notions and results to type root systems.
An approximation theorem for semigroups of operators
An elementary proof of the decomposition of measures on the circle group
We give an elementary proof for the case of the circle group of the theorem of O. Hatori and E. Sato, which states that every measure on a compact abelian group G can be decomposed into a sum of two measures with a natural spectrum and a discrete measure.
An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators.
An example of a generalized completely continuous representation of a locally compact group
There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image of the -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.
An Example of a Non Nuclear C*-Algebra, which has the Metric Approximation Property.
An example of a positive semidefinite double sequence which is not a moment sequence
The first explicit example of a positive semidefinite double sequence which is not a moment sequence was given by Friedrich. We present an example with a simpler definition and more moderate growth as .
An explicit construction of the K-finite vectors in the discrete series for an isotropic semisimple symmetric space
An extension of a theorem of F. Forelli.
An extension of deLeeuw’s theorem to the -dimensional rotation group
We study a method of approximating representations of the group by those of the group . As a consequence we establish a version of a theorem of DeLeeuw for Fourier multipliers of that applies to the “restrictions” of a function on the dual of to the dual of .
An extension of the spectral mapping theorem.
An extremal set of uniqueness?
An F. and M. Riesz theorem for bounded symmetric domains
We generalize the classical F. and M. Riesz theorem to metrizable compact groups whose center contains a copy of the circle group. Important examples of such groups are the isotropy groups of the bounded symmetric domains.The proof uses a criterion for absolute continuity involving spaces with : A measure on a compact metrisable group is absolutely continuous with respect to Haar measure on if for some a certain subspace of which is related to has sufficiently many continuous linear...
An F. and M. Riesz theorem for compact Lie groups.
An semigroup of zero measure which contains a translate of every countable set