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Rotation invariant ultradistributions

Dorde Vuckovic UGent and Jasson Vindas Diaz UGent (2017) Generalized functions and Fourier analysis. In Operator Theory : Advances and Applications 260. p.253-267
abstract
We prove that an ultradistribution is rotation invariant if and only if it coincides with its spherical mean. For it, we study the problem of spherical representations of ultradistributions on $\mathbb{R}^{n}$. Our results apply to both the quasianalytic and the non-quasianalytic case.
Please use this url to cite or link to this publication:
author
organization
year
type
bookChapter
publication status
published
subject
keyword
Rotation invariant, spherical means, ultradistributions, hyperfunctions, spherical representations, spherical harmonics
book title
Generalized functions and Fourier analysis
editor
Michael Oberguggenberger, Joachim Toft, Jasson Vindas Diaz UGent and Patrik Wahlberg
series title
Operator Theory : Advances and Applications
volume
260
pages
253 - 267
publisher
Springer
place of publication
Cham, Switzerland
ISSN
0255-0156
ISBN
9783319519104
DOI
10.1007/978-3-319-51911-1_15
language
English
UGent publication?
yes
classification
B2
additional info
dedicated to Stevan Pilipović on the occasion of his 65th birthday
copyright statement
I have transferred the copyright for this publication to the publisher
id
8520067
handle
http://hdl.handle.net/1854/LU-8520067
date created
2017-05-10 20:53:40
date last changed
2017-09-06 08:22:19
@incollection{8520067,
  abstract     = {We prove that an ultradistribution is rotation invariant if and only if it coincides with its spherical mean. For it, we study the problem of spherical representations of ultradistributions on \${\textbackslash}mathbb\{R\}\^{ }\{n\}\$. Our results apply to both the quasianalytic and the non-quasianalytic case.},
  author       = {Vuckovic, Dorde and Vindas Diaz, Jasson},
  booktitle    = {Generalized functions and Fourier analysis},
  editor       = {Oberguggenberger, Michael and Toft, Joachim and Vindas Diaz, Jasson and Wahlberg, Patrik},
  isbn         = {9783319519104},
  issn         = {0255-0156},
  keyword      = {Rotation invariant,spherical means,ultradistributions,hyperfunctions,spherical representations,spherical harmonics},
  language     = {eng},
  pages        = {253--267},
  publisher    = {Springer},
  series       = {Operator Theory : Advances and Applications},
  title        = {Rotation invariant ultradistributions},
  url          = {http://dx.doi.org/10.1007/978-3-319-51911-1\_15},
  volume       = {260},
  year         = {2017},
}

Chicago
Vuckovic, Dorde, and Jasson Vindas Diaz. 2017. “Rotation Invariant Ultradistributions.” In Generalized Functions and Fourier Analysis, ed. Michael Oberguggenberger, Joachim Toft, Jasson Vindas Diaz, and Patrik Wahlberg, 260:253–267. Cham, Switzerland: Springer.
APA
Vuckovic, D., & Vindas Diaz, J. (2017). Rotation invariant ultradistributions. In Michael Oberguggenberger, J. Toft, J. Vindas Diaz, & P. Wahlberg (Eds.), Generalized functions and Fourier analysis (Vol. 260, pp. 253–267). Cham, Switzerland: Springer.
Vancouver
1.
Vuckovic D, Vindas Diaz J. Rotation invariant ultradistributions. In: Oberguggenberger M, Toft J, Vindas Diaz J, Wahlberg P, editors. Generalized functions and Fourier analysis. Cham, Switzerland: Springer; 2017. p. 253–67.
MLA
Vuckovic, Dorde, and Jasson Vindas Diaz. “Rotation Invariant Ultradistributions.” Generalized Functions and Fourier Analysis. Ed. Michael Oberguggenberger et al. Vol. 260. Cham, Switzerland: Springer, 2017. 253–267. Print.