Advanced

On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions

Englis, M; Lukkassen, D; Peetre, Jaak LU and Persson, L E (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:
author
organization
publishing date
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
2007-10-22 08:55:37
date last changed
2017-12-10 04:25:34
@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},
  volume       = {570},
  year         = {2004},
}