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Ultradistributional boundary values of harmonic functions on the sphere

Dorde Vuckovic UGent and Jasson Vindas Diaz UGent (2018) Journal of Mathematical Analysis and Applications. 457(1). p.533-550
abstract
We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calder\'{o}n and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Harmonic functions on the unit ball, boundary values on the sphere, partial derivatives of spherical harmonics, support of ultradistributions, ultradifferentiable functions, Abel summabiity
journal title
Journal of Mathematical Analysis and Applications
J. Math. Anal. Appl.
volume
457
issue
1
pages
18 pages
ISSN
0022-247X
DOI
10.1016/j.jmaa.2017.08.035
UGent publication?
yes
classification
U
copyright statement
I have transferred the copyright for this publication to the publisher
id
8532263
handle
http://hdl.handle.net/1854/LU-8532263
date created
2017-09-25 17:50:59
date last changed
2017-10-09 13:43:10
@article{8532263,
  abstract     = {We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calder{\textbackslash}'\{o\}n and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.},
  author       = {Vuckovic, Dorde and Vindas Diaz, Jasson},
  issn         = {0022-247X},
  journal      = {Journal of Mathematical Analysis and Applications},
  keyword      = {Harmonic functions on the unit ball,boundary values on the sphere,partial derivatives of spherical harmonics,support of ultradistributions,ultradifferentiable functions,Abel summabiity},
  number       = {1},
  pages        = {533--550},
  title        = {Ultradistributional boundary values of harmonic functions on the sphere},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2017.08.035},
  volume       = {457},
  year         = {2018},
}

Chicago
Vuckovic, Dorde, and Jasson Vindas Diaz. 2018. “Ultradistributional Boundary Values of Harmonic Functions on the Sphere.” Journal of Mathematical Analysis and Applications 457 (1): 533–550.
APA
Vuckovic, D., & Vindas Diaz, J. (2018). Ultradistributional boundary values of harmonic functions on the sphere. Journal of Mathematical Analysis and Applications, 457(1), 533–550.
Vancouver
1.
Vuckovic D, Vindas Diaz J. Ultradistributional boundary values of harmonic functions on the sphere. Journal of Mathematical Analysis and Applications. 2018;457(1):533–50.
MLA
Vuckovic, Dorde, and Jasson Vindas Diaz. “Ultradistributional Boundary Values of Harmonic Functions on the Sphere.” Journal of Mathematical Analysis and Applications 457.1 (2018): 533–550. Print.