On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions
(2004) In Journal für Die Reine und Angewandte Mathematik 570. p.89-129- Abstract
- We 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 Omegasubset ofR(n) whose boundary values belong to the Sobolev space H-s(partial derivativeOmega), and also obtain generalizations of this formula when instead of harmonic functions one considers functions annihilated by a given elliptic partial differential operator. Further, we compute the reproducing kernels explicitly in several examples, which leads to an occurrence of new special functions. Some spaces of caloric functions are also briefly considered.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/276225
- author
- Englis, M ; Lukkassen, D ; Peetre, Jaak LU and Persson, L E
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal für Die Reine und Angewandte Mathematik
- volume
- 570
- pages
- 89 - 129
- publisher
- De Gruyter
- external identifiers
-
- wos:000221793400003
- scopus:2942659526
- ISSN
- 0075-4102
- DOI
- 10.1515/crll.2004.035
- language
- English
- LU publication?
- yes
- id
- 7039245a-85d6-4946-9e72-3c3a8cfed77f (old id 276225)
- date added to LUP
- 2016-04-01 15:27:34
- date last changed
- 2022-01-28 05:27:09
@article{7039245a-85d6-4946-9e72-3c3a8cfed77f, abstract = {{We 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 Omegasubset ofR(n) whose boundary values belong to the Sobolev space H-s(partial derivativeOmega), and also obtain generalizations of this formula when instead of harmonic functions one considers functions annihilated by a given elliptic partial differential operator. Further, we compute the reproducing kernels explicitly in several examples, which leads to an occurrence of new special functions. Some spaces of caloric functions are also briefly considered.}}, author = {{Englis, M and Lukkassen, D and Peetre, Jaak and Persson, L E}}, issn = {{0075-4102}}, language = {{eng}}, pages = {{89--129}}, publisher = {{De Gruyter}}, series = {{Journal für Die Reine und Angewandte Mathematik}}, title = {{On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions}}, url = {{http://dx.doi.org/10.1515/crll.2004.035}}, doi = {{10.1515/crll.2004.035}}, volume = {{570}}, year = {{2004}}, }