Let λ be a positive number, and let (xj : j ∈ Z) ⊂ R be a fixed Riesz-basis sequence, namely, (xj) is strictly increasing, and the set of functions {R ∋ t 7→ ej : j ∈ Z} is a Riesz basis (i.e., unconditional basis) for L2[−π,π]. Given a function f ∈ L2(R) whose Fourier transform is zero almost everywhere outside the interval [−π, π], there is a unique square-summable sequence (aj : j ∈ Z), depe...

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...

*Correspondence: [email protected] 3Faculty of Science and Technology, Tapee College, Surathani, 84000, Thailand Full list of author information is available at the end of the article Abstract In this paper, we obtain new Riesz representations of continuous linear maps associated with certain boundary value problems in the set of all closed bounded convex non-empty subsets of any Banach sp...

A two parameter family of multiresolution analyses of L 2 (R 2) each generated by three orthogonal, continuous, compactly supported scaling functions is constructed using fractal interpolation surfaces. The scaling functions remain orthogonal when restricted to certain triangles making them useful for problems with bounded domains. In the usual construction of a wavelet using a multiresolution ...

Various equivalent conditions under which a frame is a Riesz basis of a separable Hilbert space are known. See [8] among others, for instance. We add two new conditions to the list. They are inspired by the projection method proposed in [2], which approximates frame coefficients by using finite subsets of a frame. Our main approach is to transcribe anything involving a frame in a Hilbert space ...

A sequence of vectors {f1, f2, f3, . . . } in a separable Hilbert space H is said to be a Schauder basis for H if every element f ∈ H has a unique norm-convergent expansion f = ∑ cnfn. If, in addition, there exist positive constants A and B such that A ∑ |cn| ≤ ∥∥∥∑ cnfn∥∥∥2 ≤ B∑ |cn|, then we call {f1, f2, f3, . . . } a Riesz basis. In the first half of this paper, we show that every Schauder ...

In recent investigation 8] concerning the asymptotic behavior of Gram Schmidt or-thonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in L 2 (IR +) arose. In this note, we provide a suucient condition to determine whether the nonnegative translates form a Riesz system on L 2 (IR +)....

This paper gives an abstract sufficient condition on Riesz basis with parentheses property for the generators of C0-groups in Hilbert spaces whose eigenvalues are comprised of some finite unification of separable sets after taking the algebraic multiplicities into account. The condition is then applied to the closed-loop system of a serially connected string system under joint damping feedbacks...

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 ...