Fractional powers of strongly positive operators and their applications

2017 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ayman Hamad
Keyword(s):  
Positive Operators ◽  
Fractional Powers

A note on fractional powers of strongly positive operators and their applications

2019 ◽  
Vol 22 (2) ◽  
pp. 302-325 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ayman Hamad
Keyword(s):  
Banach Space ◽  
Elliptic Operators ◽  
Positive Operators ◽  
Fractional Powers ◽  
Fractional Spaces

Abstract The present paper deals with fractional powers of positive operators in a Banach space. The main theorem concerns the structure of fractional powers of positive operators in fractional spaces. As applications, the structure of fractional powers of elliptic operators is studied.

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

Convexity Inequalities for Positive Operators

Positivity ◽  
2006 ◽  
Vol 11 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Markus Haase
Keyword(s):  
Positive Operators

scholarly journals Unitarity of theories containing fractional powers of the d’Alembertian operator

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
E. C. Marino ◽  
Leandro O. Nascimento ◽  
Van Sérgio Alves ◽  
C. Morais Smith
Keyword(s):  
Fractional Powers
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