On the Harmonic Extension Approach to Fractional Powers in Banach Spaces

On the Harmonic Extension Approach to Fractional Powers in Banach Spaces

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...

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Veröffentlicht in:Fractional calculus & applied analysis 2020-08, Vol.23 (4), p.1054-1089
Hauptverfasser: Meichsner, Jan, Seifert, Christian
Format: Artikel
Sprache:eng
Schlagworte:
47A60
Abstract Harmonic Analysis
Analysis
Banach spaces
Differential equations
Dirichlet-to-Neumann operator
fractional powers
Functional Analysis
Integral Transforms
Mathematics
non-negative operator
Operational Calculus
Ordinary differential equations
Primary 47A05
Research Paper
Secondary 47D06
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Beschreibung
Zusammenfassung: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).
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2020-0055