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 |
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| container_title | Fractional calculus & applied analysis |
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| creator | Meichsner, Jan Seifert, Christian |
| description | 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). |
| doi_str_mv | 10.1515/fca-2020-0055 |
| format | Article |
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| ispartof | Fractional calculus & applied analysis, 2020-08, Vol.23 (4), p.1054-1089 |
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| subjects | 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 |
| title | On the Harmonic Extension Approach to Fractional Powers in Banach Spaces |
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