Results 61 to 70 of about 21,050 (203)

The expansion of a semigroup and a Riesz basis criterion

Journal of Differential Equations, 2005
Let \(\mathcal{A}\) be the generator for a strongly continuous semigroup \(T(t)\) on a Hilbert space \(X\). Suppose that the singular set for \(\mathcal{A}\) can be split into two parts \(\sigma(\mathcal{A})=\sigma_1(\mathcal{A})\cup\sigma_2(\mathcal{A})\), where \(\sigma_2(\mathcal{A})\) consists all isolated eigenvalues. Under the assumption that the
Xu, GQ, Yung, SP
openaire   +4 more sources

A review of a Riesz basis property for indefinite Sturm-Liouville problems [PDF]

Operators and Matrices, 2011
Consider the indefinite Sturm-Liouville problem−f ′′ = λrf, f(−1) = f(1) = 0 with an indefinite weight function r ∈ L[−1, 1] satisfying xr(x) > 0. A number of conditions for the so-called Riesz basis property are reviewed, i.e. conditions such that the eigenfunctions form a Ries basis of the Hilbert space L|r|[−1, 1].
Paul A. Binding, Andreas Fleige
openaire   +1 more source

New Inequalities and an Integral Expression for the 𝒜‐Berezin Number

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This work examines a reproducing kernel Hilbert space XF,·,· constructed on a nonempty set F. Our investigation focuses on the A‐Berezin number and the A‐Berezin norm, where A denotes a positive bounded linear operator acting on XF. For an A‐bounded linear operator B, the A‐Berezin seminorm is defined by BberA=supλ,ν∈FBu∧λ,u∧νA, where u∧λ and u∧ν are ...
Salma Aljawi, Ahad Alotaibi, Cristian Conde, Kais Feki, Ding-Xuan Zhou   +4 more
wiley   +1 more source

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I [PDF]

, 2007
We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter.
Binding, Paul, Ćurgus, Branko
core   +5 more sources

A Conforming Least Squares Approach for the Numerical Approximation of Parabolic Equations

Proceedings in Applied Mathematics and Mechanics, Volume 25, Issue 4, December 2025.
ABSTRACT We propose a least squares formulation for the numerical approximation of parabolic partial differential equations, which minimizes the residual of the equation using the natural L2(0,T;H−1(Ω))$L^2(0,T;H^{-1}(\Omega))$ norm. In particular, we avoid making regularity assumptions on the problem's data.
Michael Hinze, Christian Kahle, Michael Stahl   +2 more
wiley   +1 more source

p-Riesz bases in quasi shift invariant spaces

, 2017
Let $ 1\leq p< \infty$ and let $\psi\in L^{p}(\R^d)$. We study $p-$Riesz bases of quasi shift invariant spaces $V^p(\psi;Y)$
De Carli, Laura, Vellucci, Pierluigi
core   +1 more source

On solvability of the inverse problem for a fourth-order parabolic equation with a complex-valued coefficient

Қарағанды университетінің хабаршысы. Математика сериясы
In this paper, the inverse problem for a fourth-order parabolic equation with a variable complex-valued coefficient is studied by the method of separation of variables.
A.B. Imanbetova, A.A. Sarsenbi, B. Seilbekov   +2 more
doaj   +1 more source

Spectral Properties of Non-Self-Adjoint Perturbations for a Spectral Problem with Involution

Abstract and Applied Analysis, 2012
Full description of Riesz basis property for eigenfunctions of boundary value problems for first order differential equations with involutions is given.
Asylzat A. Kopzhassarova, Alexey L. Lukashov, Abdizhakhan M. Sarsenbi   +2 more
doaj   +1 more source

Nonlocal multipoint problem for a differential equation of $2n$-th order with operator coefficients

Karpatsʹkì Matematičnì Publìkacìï, 2021
In the article, the spectral properties of a multipoint problem for a differential operator equation of order $2n$ are studied. The operator of the problem has an infinite number of multiple eigenvalues.
Ya.O. Baranetskij, I.I. Demkiv, A.V. Solomko, O.M. Sus'   +3 more
doaj   +1 more source

A multivariate Riesz basis of ReLU neural networks

Applied and Computational Harmonic Analysis
We consider the trigonometric-like system of piecewise linear functions introduced recently by Daubechies, DeVore, Foucart, Hanin, and Petrova. We provide an alternative proof that this system forms a Riesz basis of $L_2([0,1])$ based on the Gershgorin theorem. We also generalize this system to higher dimensions $d>1$ by a construction, which avoids
Schneider, Cornelia, Vybíral, Jan
openaire   +3 more sources