Results 71 to 80 of about 429,980 (230)

Learning neural operators on Riemannian manifolds

National Science Open
Learning mappings between functions (operators) defined on complex computational domains is a common theoretical challenge in machine learning. Existing operator learning methods mainly focus on regular computational domains, and have many components ...
Chen Gengxiang, Liu Xu, Meng Qinglu, Chen Lu, Liu Changqing, Li Yingguang   +5 more
doaj   +1 more source

Linear extension operators for Sobolev spaces on radially symmetric binary trees

Advanced Nonlinear Studies, 2023
Let ...
Fefferman Charles, Klartag Bo’az
doaj   +1 more source

A General Norm on Extension of a Hilbert’s Type Linear Operator

Journal of Mathematical Extension, 2010
The main purpose of this paper is to study a general norm on extension of a Hilbert’s type linear operator in the continuous and discrete form. In addition to expressing the norm of a Hilbert’s type linear operator T : L 2 (0,∞) → L 2 (0,∞), a ...
Z. Jokar, J. Behboodian
doaj  

Maximal norm Hankel operators

Journal of Mathematical Analysis and Applications
A Hankel operator $\mathbf{H}_φ$ on the Hardy space $H^2$ of the unit circle with analytic symbol $φ$ has minimal norm if $\|\mathbf{H}_φ\|=\|φ\|_2$ and maximal norm if $\|\mathbf{H}_φ\| = \|φ\|_\infty$. The Hankel operator $\mathbf{H}_φ$ has both minimal and maximal norm if and only if $|φ|$ is constant almost everywhere on the unit circle or ...
Brevig, Ole Fredrik, Seip, Kristian
openaire   +4 more sources

On essential norm of the Neumann operator [PDF]

Mathematica Bohemica, 1992
The author gives an estimate of the essential norm of the Neumann operator. It is shown that under a deformation of the domain investigated by a diffeomorphism, which is conformal on a precisely specified part of the boundary, for the given norm there exists a norm on the space of continuous functions on the boundary of the deformated domain such that ...
openaire   +2 more sources

Density and dentability in norm-attainable classes

Scientific African
We establish the norm-denseness of the norm-attainable class NA(H) in the Banach algebra B(H), which consists of all bounded linear operators on a complex Hilbert space H. Specifically, for every O∈NA(H) and each ϵ>0, there exists O′∈B(H) such that ‖O−O′‖
Joseph Owuor, Benard Okelo, Julia Owino, Jeremiah Kinyanjui   +3 more
doaj   +1 more source

A STABLE METHOD FOR LINEAR EQUATION IN BANACH SPACES WITH SMOOTH NORMS

Ural Mathematical Journal, 2018
A stable method for numerical solution of a linear operator equation in reflexive Banach spaces is proposed. The operator and the right-hand side of the equation are assumed to be known approximately.
Andrey A. Dryazhenkov, Mikhail M. Potapov   +1 more
doaj   +1 more source

On some operator norm inequalities

Linear Algebra and its Applications, 2004
Let \(B(H)\) be the \(C^{*}\)-algebra of all bounded linear operators on a complex Hilbert space \(H\), and let \((I, \| \cdot\| _{I})\) denote a norm ideal of \(B(H)\). For \(A, B\in B(H)\), the author defines the two operators \(U_{I,A,B}(X)=AXB+BXA\) and \(V_{I,A,B}(X)=AXB-BXA\) on \(I\). Then the author obtains lower and upper bounds of \(U_{I,S,S^{
openaire   +2 more sources

Norm Attaining Operators and Pseudospectrum [PDF]

Integral Equations and Operator Theory, 2009
It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.
openaire   +3 more sources

Multiplication Operators on Weighted Banach Spaces of a Tree

, 2015
We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm.
Allen, Robert F., Craig, Isaac M.
core