scholarly journals Fractional powers of Bessel operators

2020 ◽  
pp. 377-431
Author(s):  
Elina Shishkina ◽  
Sergei Sitnik
Keyword(s):  
Fractional Powers ◽  
Bessel Operators

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.

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

Eigenvalue asymptotics for Dirac–Bessel operators

2016 ◽  
Vol 57 (6) ◽  
pp. 063507 ◽  
Author(s):  
Rostyslav O. Hryniv ◽  
Yaroslav V. Mykytyuk
Keyword(s):  
Eigenvalue Asymptotics ◽  
Bessel Operators

scholarly journals UMD-Valued Square Functions Associated with Bessel Operators in Hardy and BMO Spaces

2014 ◽  
Vol 81 (3) ◽  
pp. 319-374 ◽  
Author(s):  
Jorge J. Betancor ◽  
Alejandro J. Castro ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Square Functions ◽  
Bessel Operators ◽  
Bmo Spaces
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