Results 71 to 80 of about 8,384 (123)

Pseudo- Riesz Bases

In~\cite{holub1994bases} Holub introduced the concept of near-Riesz bases, as frames that can be considered Riesz bases for computational purposes or that exhibit certain desirable properties of Riesz bases. In this paper, we introduce a generalization of near-Riesz bases that includes sequences which are not necessarily frames.
Biswas, Deborpita, Mitkovski, Mishko
openaire   +2 more sources

Sufficient conditions for functions to form Riesz bases in L_2 and applications to nonlinear boundary-value problems

Electronic Journal of Differential Equations, 2001
We find sufficient conditions for systems of functions to be Riesz bases in $L_2(0,1)$. Then we improve a theorem presented in [13] by showing that a ``standard'' system of solutions of a nonlinear boundary-value problem, normalized to 1, is a Riesz ...
Peter E. Zhidkov
doaj  

Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials

Journal of Inequalities and Applications, 2016
In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out.
Ting Cheng, Xiaoyuan Yang
doaj   +1 more source

An Operator Based Approach to Irregular Frames of Translates

Mathematics, 2019
We consider translates of functions in L 2 ( R d ) along an irregular set of points, that is, { ϕ ( · − λ k ) } k ∈ Z —where ϕ is a bandlimited function.
Peter Balazs, Sigrid Heineken
doaj   +1 more source

Compressive Space-Time Galerkin Discretizations of Parabolic Partial Differential Equations [PDF]

, 2015
We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on the bi-infinite time axis.
Larsson, Stig, Schwab, Christoph
core   +1 more source

Riesz bases from orthonormal bases by replacement

, 2018
Given an orthonormal basis $ {\mathcal V}= \{v_j\} _{j\in N}$ in a separable Hilbert space $H$ and a set of unit vectors $ {\mathcal B}=\{w_j\}_{j\in N}$, we consider the sets $ {\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\, v_N$ with vectors $w_1,\, ...,\, w_N$.
De Carli, Laura, Edward, Julian
openaire   +2 more sources

On the Riesz Means of Expansion by Riesz Bases Formed by Eigen Functions for the Ordinary Differential Operator of 2mth Order

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017
  The aim of this paper is to prove a theorem on the Riesz means of expansions with respect to Riesz bases, which extends the previous results of [1] and [2] on the Schrödinger operator and the ordinary differential operator of 4-th order to the ...
A. A. Aswhad
doaj  

Wavelet Galerkin method for fractional elliptic differential equations [PDF]

, 2014
Under the guidance of the general theory developed for classical partial differential equations (PDEs), we investigate the Riesz bases of wavelets in the spaces where fractional PDEs usually work, and their applications in numerically solving fractional ...
Deng, Weihua, Lin, Yuwei, Zhang, Zhijiang   +2 more
core  

Well-posedness and stability analysis of hybrid feedback systems using Shkalikov's theory [PDF]

Opuscula Mathematica, 2006
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space.
Piotr Grabowski
doaj  

Riesz bases in quaternionic Hilbert spaces

, 2019
10 Pages.
Sharma, S. K., Virender, Kaushik, S. K.
openaire   +2 more sources