On the harmonic extension approach to fractional powers in Banach spaces

Publikationstyp
Journal Article
Date Issued
2020-08-01
Sprache
English
Author(s)
Meichsner, Jan  
Seifert, Christian  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/7663
Journal
Fractional calculus and applied analysis  
Volume
23
Issue
4
Start Page
1054
End Page
1089
Citation
Fractional calculus and applied analysis 23 (4): 1054-1089 (2020-08-01)
Publisher DOI
10.1515/fca-2020-0055
Scopus ID
2-s2.0-85092922186
ArXiv ID
1905.06779v3
We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing the harmonic extension we prove existence and uniqueness of a bounded solution (i.e. of the harmonic extension).
Subjects
And Phrases: fractional powers
Dirichlet-to-Neumann operator
Non-negative operator
Mathematics - Functional Analysis
Mathematics - Functional Analysis
47A05, 47D06, 47A60