On the Hausdorff-Young Theorem for Amalgams.
On the Hausdorff-Young theorem for commutative hypergroups
We study the Hausdorff-Young transform for a commutative hypergroup K and its dual space K̂ by extending the domain of the Fourier transform so as to encompass all functions in and respectively, where 1 ≤ p ≤ 2. Our main theorem is that those extended transforms are inverse to each other. In contrast to the group case, this is not obvious, since the dual space K̂ is in general not a hypergroup itself.
On the image of a generalized -plane transform on .
On the inverse Abel transforms for certain Riemannian symmetric spaces of rank 2.
On the Levy-Chintschin formula on locally compact maximally almost periodic groups.
On the Multiresolution analysis of abstract Hilbert spaces
On the notion of virtual amenability for groups
On the o-Spektrum of Regular Operators and the Spectrum of Measures.
On the Paley-Wiener theorem.
On the Plancherel Measure for Linear Lie Groups of Rank One.
On the product formula on noncompact Grassmannians
We study the absolute continuity of the convolution of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of...
On the product theory of singular integrals.
We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in...
On the projectivity and flatness of some group modules
In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.
On the Property P... of Locally Compact Groups
On the Proportionality of Covolumes of Discrete Subgroups.
On the Range of the Fourier Transform Associated with the Spherical Mean Operator
We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.
On the range of the Fourier transform connected with Riemann-Liouville operator
We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
On the Relation between Amenability of Locally Compact Groups and the Norms of Convolution Operators.
On the relation between Gaussian measures and convolution semigroups of local type.
On the relationships between Fourier-Stieltjes coefficients and spectra of measures
We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.