Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators

2018 ◽  
Vol 234 ◽  
pp. 1-19
Author(s):  
Athanasios G. Georgiadis ◽  
Morten Nielsen
Keyword(s):  
Spectral Multipliers ◽  
Adjoint Operators

scholarly journals Spectral Multipliers of Self-Adjoint Operators on Besov and Triebel–Lizorkin Spaces Associated to Operators

2019 ◽  
Author(s):  
The Anh Bui ◽  
Xuan Thinh Duong
Keyword(s):  
Heat Kernel ◽  
Hardy Spaces ◽  
Adjoint Operator ◽  
Space Of Homogeneous Type ◽  
Multiplier Theorem ◽  
Homogeneous Type ◽  
Spectral Multipliers ◽  
Spectral Multiplier ◽  
Gaussian Estimate ◽  
Adjoint Operators

Abstract Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ that satisfies a Gaussian estimate on its heat kernel. In this paper we prove a Hörmander-type spectral multiplier theorem for $L$ on the Besov and Triebel–Lizorkin spaces associated to $L$. Our work not only recovers the boundedness of the spectral multipliers on $L^p$ spaces and Hardy spaces associated to $L$ but also is the 1st one that proves the boundedness of a general spectral multiplier theorem on Besov and Triebel–Lizorkin spaces.

Localization of the spectrum of certain non-self-adjoint operators

1968 ◽  
Vol 3 (4) ◽  
pp. 264-266
Author(s):  
M. M. Gekhtman
Keyword(s):  
Adjoint Operators

scholarly journals Singular Perturbations of Self-Adjoint Operators

2003 ◽  
Vol 6 (4) ◽  
pp. 349-384 ◽  
Author(s):  
Vladimir Derkach ◽  
Seppo Hassi ◽  
Henk de Snoo
Keyword(s):  
Singular Perturbations ◽  
Adjoint Operators

scholarly journals Functions of perturbed tuples of self-adjoint operators

2012 ◽  
Vol 350 (7-8) ◽  
pp. 349-354 ◽  
Author(s):  
Fedor Nazarov ◽  
Vladimir Peller
Keyword(s):  
Adjoint Operators

M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator

2015 ◽  
Vol 15 (3) ◽  
pp. 373-389
Author(s):  
Oleg Matysik ◽  
Petr Zabreiko
Keyword(s):  
Hilbert Space ◽  
Iterative Methods ◽  
Critical Case ◽  
Adjoint Operator ◽  
Successive Approximations ◽  
Operator Equations ◽  
Ill Posed ◽  
Linear Problems ◽  
Adjoint Operators ◽  
Linear Operator Equations

AbstractThe paper deals with iterative methods for solving linear operator equations ${x = Bx + f}$ and ${Ax = f}$ with self-adjoint operators in Hilbert space X in the critical case when ${\rho (B) = 1}$ and ${0 \in \operatorname{Sp} A}$. The results obtained are based on a theorem by M. A. Krasnosel'skii on the convergence of the successive approximations, their modifications and refinements.

Sign in / Sign up

Export Citation Format

Share Document