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Strong boundary values : independence of the defining function and spaces of test functions

Jean-Pierre Rosay, Edgar Lee Stout (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Ferenc Weisz (1996)

Studia Mathematica

The martingale Hardy space H p ( [ 0 , 1 ) 2 ) and the classical Hardy space H p ( 2 ) are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from H p to L p (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a...

Strong summability of Ciesielski-Fourier series

Ferenc Weisz (2004)

Studia Mathematica

A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).

Sufficient conditions for the spectrality of self-affine measures with prime determinant

Jian-Lin Li (2014)

Studia Mathematica

Let μ M , D be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of μ M , D when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for μ M , D to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.

Sur le diamètre transfini entier d'un intervalle réel

Francesco Amoroso (1990)

Annales de l'institut Fourier

En utilisant à la fois la théorie des polynômes orthogonaux et des arguments élémentaires de géométrie des nombres, nous donnons ici des nouveaux encadrements pour le diamètre transfini entier d’un intervalle I d’extrémités rationnelles. Ces encadrements dépendent explicitement de la longueur de I et des dénominateurs de ses extrémités.

Sur l'existence des analyses multi-résolutions en théorie des ondelettes.

Pierre Gilles Lemarie-Rieusset (1992)

Revista Matemática Iberoamericana

On montre qu'une base d'ondelettes (ψj,k) de L2(R) avec une fonction mère ψ höldérienne à support compact provient nécessairement d'une analyse multi-résolution. La fonction-père φ a alors la même régularité que la fonction ψ et peut être choisie à support compact.

The Affine Frame in p -adic Analysis

Ming Gen Cui, Huan Min Yao, Huan Ping Liu (2003)

Annales mathématiques Blaise Pascal

In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of p -adic number, hence provide new mathematic tools for application of p -adic analysis.

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