Geodesic
Pointwise Fourier inversion of distributions on spheres
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 1059-1070 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Given a distribution $T$ on the sphere we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $\xi $ of the sphere and we show that if $T$ has the value $\tau $ at $\xi $, then the Fourier-Laplace series of $T$ at $\xi $ is Abel-summable to $\tau $.
Given a distribution $T$ on the sphere we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $\xi $ of the sphere and we show that if $T$ has the value $\tau $ at $\xi $, then the Fourier-Laplace series of $T$ at $\xi $ is Abel-summable to $\tau $.
DOI : 10.21136/CMJ.2017.0403-16
Classification : 42C10, 46F12
Keywords: distribution; sphere; Fourier-Laplace series; Abel summability 
@article{10_21136_CMJ_2017_0403_16,
     author = {Gonz\'alez Vieli, Francisco Javier},
     title = {Pointwise {Fourier} inversion of distributions on spheres},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1059--1070},
     year = {2017},
     volume = {67},
     number = {4},
     doi = {10.21136/CMJ.2017.0403-16},
     mrnumber = {3736019},
     zbl = {06819573},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0403-16/}
}
TY  - JOUR
AU  - González Vieli, Francisco Javier
TI  - Pointwise Fourier inversion of distributions on spheres
JO  - Czechoslovak Mathematical Journal
PY  - 2017
SP  - 1059
EP  - 1070
VL  - 67
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0403-16/
DO  - 10.21136/CMJ.2017.0403-16
LA  - en
ID  - 10_21136_CMJ_2017_0403_16
ER  - 
%0 Journal Article
%A González Vieli, Francisco Javier
%T Pointwise Fourier inversion of distributions on spheres
%J Czechoslovak Mathematical Journal
%D 2017
%P 1059-1070
%V 67
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0403-16/
%R 10.21136/CMJ.2017.0403-16
%G en
%F 10_21136_CMJ_2017_0403_16
González Vieli, Francisco Javier. Pointwise Fourier inversion of distributions on spheres. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 1059-1070. doi: 10.21136/CMJ.2017.0403-16

[1] Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory. Graduate Texts in Mathematics 137, Springer, New York (2001). | DOI | MR | JFM

[2] Estrada, R., Kanwal, R. P.: Distributional boundary values of harmonic and analytic functions. J. Math. Anal. Appl. 89 (1982), 262-289. | DOI | MR | JFM

[3] Vieli, F. J. González: Fourier inversion of distributions on the sphere. J. Korean Math. Soc. 41 (2004), 755-772. | DOI | MR | JFM

[4] Groemer, H.: Geometric Applications of Fourier Series and Spherical Harmonics. Encyclopedia of Mathematics and Its Applications 61, Cambridge University Press, Cambridge (1996). | DOI | MR | JFM

[5] Kostadinova, S., Vindas, J.: Multiresolution expansions of distributions: pointwise convergence and quasiasymptotic behavior. Acta Appl. Math. 138 (2015), 115-134. | DOI | MR | JFM

[6] Łojasiewicz, S.: Sur la fixation des variables dans une distribution. Stud. Math. 17 (1958), 1-64 French. | DOI | MR | JFM

[7] Stein, E. M., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton Mathematical Series 32, Princeton University Press, Princeton (1971). | DOI | MR | JFM

[8] Vindas, J., Estrada, R.: Distributional point values and convergence of Fourier series and integrals. J. Fourier Anal. Appl. 13 (2007), 551-576. | DOI | MR | JFM

[9] Walter, G.: Pointwise convergence of distribution expansions. Stud. Math. 26 (1966), 143-154. | DOI | MR | JFM

[10] Walter, G. G., Shen, X.: Wavelets and Other Orthogonal Systems. Studies in Advanced Mathematics, Chapman & Hall/CRC, Boca Raton (2001). | MR | JFM

Cité par Sources :