On the harmonic extension approach to fractional powers in Banach spaces

Publisher DOI:	10.1515/fca-2020-0055
arXiv ID:	1905.06779v3
Title:	On the harmonic extension approach to fractional powers in Banach spaces
Language:	English
Authors:	Meichsner, Jan Seifert, Christian
Keywords:	And Phrases: fractional powers; Dirichlet-to-Neumann operator; Non-negative operator; Mathematics - Functional Analysis; Mathematics - Functional Analysis; 47A05, 47D06, 47A60
Issue Date:	1-Aug-2020
Source:	Fractional calculus and applied analysis 23 (4): 1054-1089 (2020-08-01)
Abstract (english):	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).
URI:	http://hdl.handle.net/11420/7663
ISSN:	1311-0454
Journal:	Fractional calculus and applied analysis
Institute:	Mathematik E-10
Document Type:	Article
Appears in Collections:	Publications without fulltext

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