1. G. H. Hardy and M. Riesz, The general theory of Dirichlet's series, London, 1915. 2. E. Kogbetliantz, Sur la sommation des séries divergentes par les moyennes simples et doubles, Ann. École Norm. (3) vol. 42 (1925) pp. 193-216. 3. Otto Szász, Verallgemeinerung eines Littlewood'sehen Salzes über Potenzreihen, J. London Math. Soc. vol. 3 (1928) pp. 254-262. 4. A. Zygmund, Remarque sur la somma...

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

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...