In this paper the localization properties of the spectral expansions of distributions related to the self adjoint extension of the Schrodinger operator are investigated. Spectral decompositions of the distributions and some classes of distributions are defined. Estimations for Riesz means of the spectral decompositions of the distributions in the norm of the Sobolev classes with negative order ...

Introduction Raman spectroscopy is a vibrational spectroscopic technique, based on inelastic scattering of monochromatic light. This technique can provide valuable information about biomolecular changes, associated with neoplastic transformation. The purpose of this study was to find Raman spectral markers for distinguishing normal samples from cancerous ones in different tissues. Materials and...

The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel (t − s)−μ with 0 < μ < 1. In this work, we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth. We provide a rigorous error analysis for the spectral methods, which shows that both th...

Let Ω⊂ Rd be a bounded or an unbounded Lipschitz domain. In this note we address the problem of continuation of functions from the Sobolev space H1(Ω) up to functions in the Sobolev space H1(Rd) via a linear operator. The minimal possible norm of such an operator is estimated from below in terms of spectral properties of self-adjoint Robin Laplacians on domains Ω and Rd \Ω . Another estimate of...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

Reenement equations play an important role in computer graphics and wavelet analysis. In this paper we investigate multivariate reenement equations associated with a dila-tion matrix and a nitely supported reenement mask. We characterize the L p-convergence of a subdivision scheme in terms of the p-norm joint spectral radius of a collection of matrices associated with the reenement mask. In par...

Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one in this note when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewis...

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being chosen based on the leverage scores of its row and column, and then involves weighted alternating minimization over the factored form of the intended low-ra...

In this paper, we obtain the spectral norm and eigenvalues of circulant matrices with Horadam’s numbers. Furthermore, we define the semicirculant matrix with these numbers and give the Euclidean norm of this matrix. 2000 Mathematics Subject Classification: 11B39; 15A36; 15A60; 15A18.

Some new perturbation bounds of the positive (semi) definite polar factor and the (sub) unitary polar factor for the (generalized) polar decomposition under the general unitarily invariant norm and the spectral norm are presented. By applying our new bounds to the weighted cases, the known perturbation bounds for the weighted polar decomposition are improved. 2014 Elsevier Inc. All rights reser...