This paper is concerned with the numerical solutions of a variable-order space-time fractional reaction-diffusion model. The space-time fractional derivative is considered in the sense of Riesz-Feller, the system is defined by replacing the second order space derivatives with the variable Riesz-Feller derivatives. The problem is solved by an explicit finite difference method. Finally, simulatio...

The Feichtinger Conjecture, if true, would have as a corollary that for each set E ⊂ T and Λ ⊂ Z, there is a partition Λ1, . . . ,ΛN of Z such that for each 1 ≤ i ≤ N , {exp(2πixλ) : λ ∈ Λi} is a Riesz sequence. In this paper, sufficient conditions on sets E ⊂ T and Λ ⊂ R are given so that {exp(2πixλ)1E : λ ∈ Λ} can be uniformly partitioned into Riesz sequences.

We introduce and study a topological structure over vectorial and Riesz MV-algebras, similar to metric spaces. Continuous functions with values in these spaces are studied and a fix point theorem is obtained. Moreover we introduce the concept of derivative and integral of MV-valued functions; i.e. functions with values in a Riesz MV-algebra. Finally we present two applications. 2003 Elsevier In...

Let Rα be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by α ∈ C. I give an elementary proof of the necessary and sufficient condition for Rα to be a locally finite complex measure (= complex Radon measure). Soit Rα la distribution de Riesz sur une algèbre de Jordan euclidienne simple, paramétrisée par α ∈ C. Je donne une démonstration élémentaire de la condition néc...

We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on R. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of R. Moreover, we discuss the problem of the flat polynomials in this setting. Dedicated to Professors Jean-Paul Thouvenot and Bernard Host. AMS S...

In this paper we answer Open Problem 2 of Goodearl’s book on partially ordered abelian groups in the case of partially ordered simple groups. As a consequence, we obtain a version of the Theorem of structure of dimension groups in the case of simple Riesz groups. Also, we give a method for constructing torsion-free strictly perforated simple Riesz groups of rank one, and we see that every dense...

In this note we improve the known L p-bounds for Bochner-Riesz operators and their maximal operators.

Let L be an Archimedean Riesz space with a weak order unit u. A sufficient condition under which Dedekind [σ-]completeness of the principal ideal Au can be lifted to L is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of C(X)-spaces. Similar results are obtained for the Riesz spaces Bn(T ), n = 1, 2, . . . , of all functions o...

We consider a functional on the Wiener space which is smooth and not degenerated in Malliavin sense and we give a criterion for the strict positivity of the density, that we can use to state lower bounds as well. The results are based on the representation of the density in terms of the Riesz transform introduced in Malliavin and Thalmaier bib:[M.T] [16] and on the estimates of the Riesz transf...

The well-known necessary and sufficient criteria for the Riemann hypothesis of M. Riesz and of Hardy and Littlewood, based on the order of certain entire functions on the positive real axis, are here embedded in a general theorem for a class of entire functions, which in turn is seen to be a consequence of a rather transparent convolution criterion. Some properties of the convolutions involved ...