Let G be a countable group of unitary operators on a complex separable Hilbert space H. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.

The Fejér-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrixand operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum’s operator generalization of the classical Fejér-Riesz theorem. Mathematics Subject Classification (2000). Primary 47A68; Secondary 60G25, 47A56, 47B35, 42A05, 32A70, 30E99.

We use the matrix-valued Fejér–Riesz lemma for Laurent polynomials to characterize when a univariate shift-invariant space has a local orthonormal shift-invariant basis, and we apply the above characterization to study local dual frame generators, local orthonormal bases of wavelet spaces, and MRA-based affine frames. Also we provide a proof of the matrixvalued Fejér–Riesz lemma for Laurent pol...

Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment problem approach, the Riesz basis of invariant subspaces and the Riesz basis of family of exponentials.

The compact operators on the Riesz sequence space 1 ∞ have been studied by Başarır and Kara, “IJST (2011) A4, 279-285”. In the present paper, we will characterize some classes of compact operators on the normed Riesz sequence spaces and by using the Hausdorff measure of noncompactness.

Using the Riesz basis approach, we study a sandwich beam that is composed of an outer stiff layer and a compliant middle layer. The dynamic behavior and analyticity of the system are obtained based on a detailed spectral analysis and Riesz basis generation. As a consequence, the analyticity of the solution and the exponential stability of the system are concluded.

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

For p-subordinate perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without parentheses is obtained under an additional a priori assumption on the spectrum of the perturbed operator. The results are applied to two classes of block operator mat...

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

Over the last decades, one field of intense research activity has been the study of extremals of integral functionals. The Riesz-type kind has attracted growing attention and played a crucial role in the resolution of Choquard’s conjecture in a breakthrough paper by E. H. Lieb [1]. The determination of cases of equality in the Riesz-rearrangement inequality has also received a large amount of i...