We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin’s Theorem on 1/4 in the mean or in a Theorem of Bogmér, Horváth, Joó and Seip. An application is discussed, ...

1. Compact operators on Banach spaces 2. Appendix: total boundedness and Arzela-Ascoli [Fredholm 1900/1903] treated compact operators as limiting cases of finite-rank operators. [1] [Riesz 1917] defined and made direct use of the compactness condition, more apt for Banach spaces. See [Riesz-Nagy 1952] for extensive discussion in the Hilbert-space situation, and many references to original paper...

A linear feedback control is designed regardless of dissipativity of the system for the stabilization of a flexible beam with a tip rigid body. The Riesz basis approach is adopted in the investigation. It is shown that the closed loop system is a Riesz spectral system and as consequences, the exponential stability, the observability and the controllability of the system are concluded. Finally, ...

We derive the complete asymptotic expansion in terms of powers of N for the Riesz s-energy of N equally spaced points on the unit circle as N →∞. For s ≥ −2, such points form optimal energy N -point configurations with respect to the Riesz potential 1/r, s 6= 0, where r is the Euclidean distance between points. By analytic continuation we deduce the expansion for all complex values of s. The Ri...

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...