In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop ...

One of the best ways of studying ordered algebraic structures is through their spectra. The three well-known spectra usually considered are the Brumfiel, Keimel, and the maximal spectra. The pointfree versions of these spectra were studied by B. Banaschewski for f -rings. Here, we give the pointfree versions of the Keimel and the maximal spectra for Riesz spaces. Moreover, we briefly mention ho...

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 ...

Shift-invariance \ berization techniques" are applied for the study of the synthesis and analysis operators of a ne (wavelet) systems. In this approach, one has rst to circumvent the fact that a ne systems are not shift-invariant. The results obtained include characterizations of the Bessel property, the Riesz basis property and the frame property of such sets in terms of the behaviour of simpl...

(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...

We show that the conjectured generalization of the BourgainTzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent sequences. We further show that the two conjectures are impl...

We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and Vázquez [13, 14], where the pressure is obtained as a Riesz potential associated to the density. We take advantage of the displacement convexity of the Riesz potential in one dimension to show a functional inequality involving the entropy, entropy...

More generally, in the first claim we can replace the Lp(Q) norm with any norm || · || on F with the Riesz property, which is that |f | ≤ |g| (pointwise) implies ||f || ≤ ||g||. For the second claim, we can use any norm that has the Riesz property and for which the norm of the constant function f ≡ 1 is 1, which is clearly satisfied by Lp(Q) when Q is a probability measure. With these more gene...

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,...

For f ∈ S(R), we consider the Bochner-Riesz operator R of index δ > 0 defined by R̂δf(ξ) = (1− |ξ|)+ f̂(ξ). Then we prove the Bochner-Riesz conjecture which states that if δ > max{d|1/p − 1/2| − 1/2, 0} and p > 1 then R is a bounded operator from L(R) into L(R); moreover, if δ(p) = d(1/p − 1/2) − 1/2 and 1 < p < 2d/(d + 1), then Rδ(p) is a bounded operator from L(R) into L(R).