On harmonic separation
On integer-valued Fourier-Stieltjes transforms on a LCA group with a certain direction.
On Ito-Nisio type theorems for DS-groups.
On the Convergence and Divergence Behaviour of Approximation Processes in Homogeneous Banach Spaces.
On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.
On the Hausdorff-Young Theorem for Amalgams.
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.
On the structure of monoids of admissible translates of probability measures.
On the vector-valued Fourier transform and compatibility of operators
Let be a locally compact abelian group and let 1 < p ≤ 2. ’ is the dual group of , and p’ the conjugate exponent of p. An operator T between Banach spaces X and Y is said to be compatible with the Fourier transform if admits a continuous extension . Let denote the collection of such T’s. We show that for any and positive integer n. Moreover, if the factor group of by its identity component is a direct sum of a torsion-free group and a finite group with discrete topology then .
On the Wiener-Eberlein theorem
On Weyl Operators over Locally Compact Abelian Groups.
Opérateurs pseudo-différentiels sur certains groupes totalement discontinus
Perturbation Classes of Semi-Fredholm Operators.
Perturbations de suites presque-périodiques de nombres réels et mesures étranges sur la droite
Pointwise convergence of the Fourier transform on locally compact abelian groups.
We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φU * f(y) = f (y) almost everywhere for any function f in the space (LP, l∞)(G) (hence in LP(G)), 2 ≤ p ≤ ∞, where {φU} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q.
Power bounded restrictions of Fourier-Stieltjes transforms.
p-Pseudomeasures and Closed Subgroups.
Quantizations and symbolic calculus over the -adic numbers
We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the -adic numbers. We apply this theory to the study of elliptic operators over the -adic numbers and determine their asymptotic spectral behavior.
Recent developments on the F. and M. Riesz theorem
Recovery of band-limited functions on locally compact Abelian groups from irregular samples
Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative...