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 give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz -difference sequence space , . For this purpose, we apply the Hausdorff measure of noncompactness and use some results.

Assuming that a Nemytskii operator maps a subset of the space of bounded variation functions in the sense of Riesz into another space of the same type, and is uniformly continuous, we prove that the generator of the operator is an affine function.

We give a new constructive method for finding compactly supported prewavelets in L2 spaces in the multivariate setting. This method works for any dimensional space. When this method is generalized to the Sobolev space setting, it produces a pre-Riesz basis for Hs(IR) which can be useful for applications. AMS(MOS) Subject Classifications: Primary 42C15, Secondary 42C30

A model is considered for turbulent diffusion which consists of a Riesz space fractional derivative to describe the turbulent phenomenon and also includes advection and classical diffusion. We present a first order explicit numerical method and a second order implicit numerical method to solve our problem and prove convergence results for both methods, including the derivation of stability cons...

We consider the natural generating system for a cyclic subspace of a Hilbert space generated by a dual integrable unitary representation of a countable abelian group. We prove, under mild hypothesis, that whenever the generating system is a quasi-greedy basis it must also be an unconditional Riesz basis. A number of applications to Gabor systems and to general Vilenkin systems are considered. I...

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.

Let L = −div(A(x)∇) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on Rn or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2, a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ∇(L)−1/2 on the Lp space. As an application, for 1 < p < 3+ ε, we establish the Lp boundedness...