Let θ be a Young function. Consider the space of all entire functions on with θ-exponential growth. In this Note, we are interested in the solutions of the convolution equation , called T-mean-periodic functions, where T is in the topological dual of . We show that each mean-periodic function admits an expansion as a convergent series of exponential polynomials.
Soit θ une fonction de Young. Considérons l'espace de toutes les fonctions entières sur à croissance θ-exponentielle. On s'intéresse dans cette Note aux solutions de l'équation de convolution , appelées fonctions T-moyenne-périodiques, où T est dans le dual topologique de . On montre que toute fonction moyenne-périodique admet un développement en série de polynômes exponentiels. De plus cette série est convergente pour la topologie de l'espace .
Accepted:
Published online:
Habib Ouerdiane 1; Myriam Ounaies 2
@article{CRMATH_2008__346_9-10_509_0, author = {Habib Ouerdiane and Myriam Ounaies}, title = {Expansion in series of exponential polynomials of mean-periodic functions with growth conditions}, journal = {Comptes Rendus. Math\'ematique}, pages = {509--514}, publisher = {Elsevier}, volume = {346}, number = {9-10}, year = {2008}, doi = {10.1016/j.crma.2008.03.027}, language = {en}, }
TY - JOUR AU - Habib Ouerdiane AU - Myriam Ounaies TI - Expansion in series of exponential polynomials of mean-periodic functions with growth conditions JO - Comptes Rendus. Mathématique PY - 2008 SP - 509 EP - 514 VL - 346 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2008.03.027 LA - en ID - CRMATH_2008__346_9-10_509_0 ER -
%0 Journal Article %A Habib Ouerdiane %A Myriam Ounaies %T Expansion in series of exponential polynomials of mean-periodic functions with growth conditions %J Comptes Rendus. Mathématique %D 2008 %P 509-514 %V 346 %N 9-10 %I Elsevier %R 10.1016/j.crma.2008.03.027 %G en %F CRMATH_2008__346_9-10_509_0
Habib Ouerdiane; Myriam Ounaies. Expansion in series of exponential polynomials of mean-periodic functions with growth conditions. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 509-514. doi : 10.1016/j.crma.2008.03.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.027/
[1] Complex Analysis and Special Topics in Harmonic Analysis, Springer-Verlag, New York, 1995
[2] Dirichlet series and convolution equations, Publ. RIMS, Kyoto Univ., Volume 24 (1988), pp. 783-810
[3] Complex analysis and convolution equations, Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya., vol. 54, 1989, pp. 5-111 (English transl.: Several Complex Variables. V: Complex Analysis in Partial Differential Equations and Mathematical Physics, Encycl. Math. Sci., vol. 54, 1993, pp. 1-108)
[4] A new look at interpolation theory for entire functions of one variable, Adv. in Math., Volume 33 (1979) no. 2, pp. 109-143
[5] Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle, J. Funct. Anal., Volume 171 (2000) no. 1, pp. 1-14
[6] Analysis of Numerical Methods, Dover Publications Inc., New York, 1994 (Corrected reprint of the 1966 original, Wiley, New York)
[7] Interpolation by entire functions with growth conditions, Michigan Math. J., Volume 56 (2008) no. 1
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