The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in the present paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C0 semigroup, and its spectrum consists of two branches and has two ...

(see [9] and [10]). Throughout this work, we assume that the function satis®es the following conditions: (i) j …x†j …cons:† jB…x†j=jxj1‡"; where " 0 and jB…x†j is bounded and 1-periodic function on R. (ii) P n2Z …n† eÿin converges absolutely to a function that has no zeros on ‰ÿ ; Š. It is known that conditions (i) and (ii) imply that fK…x; n†; n 2 Zg is a Riesz basis on V , with a unique biort...

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A,...

Using an abstract condition of Riesz basis generation of discrete operators in the Hilbert spaces, we show, in this paper, that a sequence of generalized eigenfunctions of an Euler– Bernoulli beam equation with a tip mass under boundary linear feedback control forms a Riesz basis for the state Hilbert space. In the meanwhile, an asymptotic expression of eigenvalues and the exponential stability...

In this paper we use the lifting scheme to construct biorthogonal spline wavelet bases on regularly refined non-uniform grids. The wavelets have at least one vanishing moment and on each resolution level they form an L2 Riesz basis. Furthermore we are interested in determining the exact range of Sobolev exponents for which the complete multilevel system forms a Riesz basis. Hereto we need to ex...

In this paper we use the standard terminology and notations of the Riesz spaces theory (see [2]). The Banach lattice of the continuous functions from a compact Hausdorff space into a Banach lattice E is denoted by C(K,E). If E = R then we write C(K) instead of C(K,E). 1 stands for the unit function in C(K). One version of the Banach–Stone theorem states that: Theorem 1. Let X and Y be compact H...

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 show that there exists a bounded subset of $\mathbb{R}$ such no system exponentials can be Riesz basis for the corresponding Hilbert space. An additional result gives lower bound constant any putative two dimensional disk.

In this note, we provide an alternative proof of C-regularity of continuous weak solutions to the system of harmonic map or heat flow of harmonic maps by Riesz potential estimates between Morrey spaces.

In this paper, we introduce the notion of δ-quasi-slowly oscillating sequences, study on δ-quasi-slowly oscillating compactness and δ-quasi-slowly oscillating continuous functions in locally normal Riesz space.