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Rotation invariant ultradistributions

Dorde Vuckovic (UGent) and Jasson Vindas Diaz (UGent)
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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.
Keywords
Rotation invariant, spherical means, ultradistributions, hyperfunctions, spherical representations, spherical harmonics

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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.
@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},
}

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