Frequency-Domain Bounds for Nonnegative, Unsharply Band-Limited Functions.
Front d'onde analytique et décomposition microlocale des distributions
On étudie en détail une décomposition microlocale analytique de la distribution suivant des distributions singulières en un seul point et dans une seule codirection. Cette décomposition est obtenue à partir d’opérateurs Fourier-Intégraux à phases complexes.On utilise ensuite cet outil pour démontrer le théorème de décomposition du front d’onde analytique des distributions. On établit également des théorèmes concernant la représentation globale des distributions comme sommes de valeurs au bord...
Function Algebras and Flows. III.
Functions from -spaces and Taylor means
Functions in -space and their approximations
Functions with Time and Frequency Gaps.
Further properties of an extremal set of uniqueness
Gauss type quadrature formulas for singular integrals
Gaussian kernels have only Gaussian maximizers.
GCD sums from Poisson integrals and systems of dilated functions
Upper bounds for GCD sums of the form are established, where is any sequence of distinct positive integers and ; the estimate for solves in particular a problem of Dyer and Harman from 1986, and the estimates are optimal except possibly for . The method of proof is based on identifying the sum as a certain Poisson integral on a polydisc; as a byproduct, estimates for the largest eigenvalues of the associated GCD matrices are also found. The bounds for such GCD sums are used to establish...
Genaue Bewertung der Approximationsfunktion aus der Klasse durch die Favardsummen
Generalization of a result for cosine series on the norm.
Generalization of a Theorem of Pati.
Generalizations of Calderón-Zygmund operators
Generalizations of the Riemann-Lebesgue and Cantor-Lebesgue lemmas
Generalizations of theorems of Fejér and Zygmund on convergence and boundedness of conjugate series
Generalized -almost periodic type functions in
In this paper, we analyze multi-dimensional quasi-asymptotically -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically -almost periodic functions and reconsider the notion of semi--periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide certain...
Generalized Herglotz theorem in vector lattices
Generalized Riesz products produced from orthonormal transforms
Let be a finite set of step functions or real valued trigonometric polynomials on = [0,1) satisfying a certain orthonormality condition. We study multiscale generalized Riesz product measures μ defined as weak-* limits of elements , where are -dimensional subspaces of L₂() spanned by an orthonormal set which is produced from dilations and multiplications of elements of and . The results involve mutual absolute continuity or singularity of such Riesz products extending previous results on...
Geodesics in the Heisenberg Group
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.