KIT | KIT-Bibliothek | Impressum | Datenschutz

Interpolation of a regular subspace complementing the span of a radially singular function

Zerulla, Konstantin ORCID iD icon


We analyze the interpolation of the sum of a subspace, consisting of regular functions, with the span of a function with $r^\alpha$-type singularity. In particular, we determine all interpolation parameters, for which the interpolation space of the subspace of regular functions is still a closed subspace. The main tool is here a result by Ivanov and Kalton on interpolation of subspaces. To apply it, we study the $K$-functional of the $r^\alpha$-singular function. It turns out that the $K$-functional possesses upper and lower bounds that have a common decay rate at zero.

Volltext §
DOI: 10.5445/IR/1000134315
Veröffentlicht am 22.06.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 06.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000134315
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 13S.
Serie CRC 1173 Preprint ; 2021/28
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter subspace interpolation, $r^\alpha$ -type singularity, K-functional, Sobolev spaces, modulus of smoothness
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page