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On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions. (English) Zbl 1053.46016

In this interesting paper, the authors give a simpler proof of the formula, due to J.-L. Lions, for the reproducing kernel of the space of harmonic functions on a domain whose boundary values belong to a Sobolev space [Proceedings of the international conference in honour of Jaak Peetre on his 65th birthday, Lund, Sweden, August 17–22, 49–59 (2002; Zbl 1129.46305)]. Some generalizations of this formula are obtained when instead of harmonic functions one considers functions annihilated by a given elliptic partial differential operator. At the end, the authors compute the reproducing kernels explicitly for some examples.

MSC:

46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
49J10 Existence theories for free problems in two or more independent variables

Citations:

Zbl 1129.46305
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References:

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