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On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions
MÚ AV ČR, Zitná 25, 11567 Prague.
Centre for Mathematical Sciences, Lund University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2004 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 570, 89-129 p.Article in journal (Refereed) Published
Abstract [en]

In an earlier work, J.-L. Lions produced a means for creating reproducing formulas for the space of harmonic functions with Sobolev boundary values on a domain in real Euclidean space. The present authors give a new proof of this result and also generalize the Lions formula to handle spaces of functions that are annihilated by an elliptic operator. The method of constructing the reproducing kernels seems to be based on the old paradigm of Aronszajn and Bergman. It is interesting to note that this model---that the kernel should take the form $$ K(x,y)=\sum_j e_j(x)·e_j(y) $$ for a suitable orthonormal basis $\{e_j\}$---goes back to the thesis of Bochner. That thesis well predates the early work of Bergman and Szegö.

Place, publisher, year, edition, pages
2004. Vol. 570, 89-129 p.
Research subject
URN: urn:nbn:se:ltu:diva-10270DOI: 10.1515/crll.2004.035Local ID: 90cc9610-a646-11db-9811-000ea68e967bOAI: diva2:983212
Validerad; 2004; 20061107 (evan)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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