Page 1 Next

## Displaying 1 – 20 of 80

Showing per page

### A law of the iterated logarithm for general lacunary series

Colloquium Mathematicae

We prove a law of the iterated logarithm for sums of the form ${\sum }_{k=1}^{N}{a}_{k}f\left({n}_{k}x\right)$ where the ${n}_{k}$ satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.

### A Littlewood-Paley inequality for arbitrary intervals.

Revista Matemática Iberoamericana

### A lower bound in the law of the iterated logarithm for general lacunary series

Studia Mathematica

We prove a lower bound in a law of the iterated logarithm for sums of the form ${\sum }_{k=1}^{N}{a}_{k}f\left({n}_{k}x+{c}_{k}\right)$ where f satisfies certain conditions and the ${n}_{k}$ satisfy the Hadamard gap condition ${n}_{k+1}/{n}_{k}\ge q>1$.

### A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series

Colloquium Mathematicae

We prove the central limit theorem for the multisequence ${\sum }_{1\le n₁\le N₁}\cdots {\sum }_{1\le {n}_{d}\le {N}_{d}}{a}_{n₁,...,{n}_{d}}cos\left(⟨2\pi m,A{₁}^{n₁}...{A}_{d}^{{n}_{d}}x⟩\right)$ where $m\in {ℤ}^{s}$, ${a}_{n₁,...,{n}_{d}}$ are reals, $A₁,...,{A}_{d}$ are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in ${\left[0,1\right]}^{s}$. The main tool is the S-unit theorem.

### About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system.

International Journal of Mathematics and Mathematical Sciences

### An estimate of the conjugate functions

Studia Mathematica

### Approximation properties of the partial sums of Fourier series of some almost periodic functions

Studia Mathematica

### Central Lacunary Sets.

Monatshefte für Mathematik

### Certain lacunary cosine series are recurrent

Studia Mathematica

Let the coefficients of a lacunary cosine series be bounded and not square-summable. Then the partial sums of the series are recurrent.

### Characterizing Sidon sets by interpolation properties of subsets

Colloquium Mathematicae

Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups containing...

### Charakterisierungen von nirgends differenzierbaren Weierstraß-Funktionen durch Replikativität.

Elemente der Mathematik

### Complex Unconditional Metric Approximation Property for ${C}_{\Lambda }\left(\right)$ spaces

Studia Mathematica

We study the Complex Unconditional Metric Approximation Property for translation invariant spaces ${C}_{\Lambda }\left(\right)$ of continuous functions on the circle group. We show that although some “tiny” (Sidon) sets do not have this property, there are “big” sets Λ for which ${C}_{\Lambda }\left(\right)$ has (ℂ-UMAP); though these sets are such that ${L}_{\Lambda }^{\infty }\left(\right)$ contains functions which are not continuous, we show that there is a linear invariant lifting from these ${L}_{\Lambda }^{\infty }\left(\right)$ spaces into the Baire class 1 functions.

Acta Arithmetica

### Dimension and Entropy of a Non-ergodic Markovian Process and its Relation to Rademacher Riesz Products.

Monatshefte für Mathematik

### Energy of measures on compact Riemannian manifolds

Studia Mathematica

We investigate the energy of measures (both positive and signed) on compact Riemannian manifolds. A formula is given relating the energy integral of a positive measure with the projections of the measure onto the eigenspaces of the Laplacian. This formula is analogous to the classical formula comparing the energy of a measure in Euclidean space with a weighted L² norm of its Fourier transform. We show that the boundedness of a modified energy integral for signed measures gives bounds on the Hausdorff...

### Ensembles de non synthèse pour certains poids dissymétriques sur la droite

Studia Mathematica

### Ensembles de Sidon topologiques

Annales de l'institut Fourier

On étudie les ensembles de Sidon d’un groupe abélien localement compact et métrisable $\Gamma$. Après avoir démontré des résultats sur la réunion, l’élargissement et la stabilité de ces ensembles lacunaires, on détaille le résultat fondamental de ce travail : lorsque le dual $G$ de $\Gamma$ est connexe, toute partie compacte d’intérieur non vide de $G$ est associée à tout ensemble de Sidon de $\Lambda$. Autrement dit, étant donné un compact $K$ d’intérieur non vide de $G$, toute fonction bornée à valeurs complexes définie sur...

### Equirépartition module 1 des suites lacunaires

Seminaire de Théorie des Nombres de Bordeaux

### Equivalence et orthogonalité des mesures aléatoires engendrées par martingales positives homogènes

Studia Mathematica

### Ergodicité et pureté des produits de Riesz

Annales de l'institut Fourier

On montre que les produits de Riesz sur le tore sont des mesures ergodiques sous une condition de lacunarité pour les fréquences, indépendamment de toute propriété arithmétique, et que cette condition est la meilleure possible de ce point de vue. On établit un critère analogue pour la propriété de pureté discutés précédemment par B. Host et l’auteur, ce qui fournit l’exemple d’une mesure pure étrangère à toutes ses translatées et en particulier non ergodique.

Page 1 Next