[Les espaces de polynômes trigonométriques avec fréquences dans un sous-groupe sont denses dans les espaces Lα]
Soit G un groupe abélien, localement compact pour une topologie séparée, H un sous-groupe fermé, Γ le groupe dual de G et μ une mesure de Borel positive ou nulle, régulière et finie sur Γ. Nous donnons des conditions nécessaires et suffisantes pour que l'ensemble des polynômes trigonométriques sur Γ avec fréquences dans H soit dense dans , .
Let G be an LCA group, H a closed subgroup, Γ the dual group of G and μ be a regular finite non-negative Borel measure on Γ. We give some necessary and sufficient conditions for the density of the set of trigonometric polynomials on Γ with frequencies from H in the space .
Accepté le :
Publié le :
@article{CRMATH_2018__356_6_586_0,
author = {Medina, Juan Miguel and Klotz, Lutz Peter and Riedel, Manfred},
title = {Density of spaces of trigonometric polynomials with frequencies from a subgroup in {\protect\emph{L}\protect\textsuperscript{\protect\emph{\ensuremath{\alpha}}}-spaces}},
journal = {Comptes Rendus. Math\'ematique},
pages = {586--593},
publisher = {Elsevier},
volume = {356},
number = {6},
year = {2018},
doi = {10.1016/j.crma.2018.04.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.04.021/}
}
TY - JOUR AU - Medina, Juan Miguel AU - Klotz, Lutz Peter AU - Riedel, Manfred TI - Density of spaces of trigonometric polynomials with frequencies from a subgroup in Lα-spaces JO - Comptes Rendus. Mathématique PY - 2018 SP - 586 EP - 593 VL - 356 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.04.021/ DO - 10.1016/j.crma.2018.04.021 LA - en ID - CRMATH_2018__356_6_586_0 ER -
%0 Journal Article %A Medina, Juan Miguel %A Klotz, Lutz Peter %A Riedel, Manfred %T Density of spaces of trigonometric polynomials with frequencies from a subgroup in Lα-spaces %J Comptes Rendus. Mathématique %D 2018 %P 586-593 %V 356 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.04.021/ %R 10.1016/j.crma.2018.04.021 %G en %F CRMATH_2018__356_6_586_0
Medina, Juan Miguel; Klotz, Lutz Peter; Riedel, Manfred. Density of spaces of trigonometric polynomials with frequencies from a subgroup in Lα-spaces. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 586-593. doi : 10.1016/j.crma.2018.04.021. http://www.numdam.org/articles/10.1016/j.crma.2018.04.021/
[1] A converse to Kluvánek's theorem, J. Fourier Anal. Appl., Volume 13 (2007) no. 2, pp. 187-195
[2] Measure theory, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser/Springer, New York, 2013
[3] Existence of Borel transversals in groups, Pac. J. Math., Volume 25 (1968), pp. 455-461
[4] Generalized sampling: from shift-invariant to u-invariant spaces, Anal. Appl., Volume 13 (2015) no. 03, pp. 303-329
[5] Sampling theorems on locally compact groups from oscillation estimates, Math. Z., Volume 255 (2007) no. 1, pp. 177-194
[6] Abstract Harmonic Analysis. Volume II – Structure and Analysis for Compact Groups. Analysis on Locally Compact Abelian Groups, Die Grundlehren der Mathematischen Wissenschaften, vol. 152, Springer-Verlag, Berlin–New York, 1970
[7] Abstract Harmonic Analysis. Volume I – Structure of Topological Groups, Integration Theory, Group Representations, Die Grundlehren der Mathematischen Wissenschaften, vol. 115, Springer-Verlag, Berlin–New York, 1979
[8] Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc., Volume 3 (1952), pp. 484-487
[9] Periodic observations of harmonizable symmetric stable processes, Probab. Math. Stat., Volume 25 (2005), pp. 289-306
[10] Sampling theorem in abstract harmonic analysis, Mat.-Fyz. Čas., Volume 15 (1965) no. 1, pp. 43-47
[11] Sampling theorems for nonstationary random processes, Trans. Amer. Math. Soc., Volume 242 (1978), pp. 225-241
[12] A sampling theorem for stationary (wide sense) stochastic processes, Trans. Amer. Math. Soc., Volume 92 (1959) no. 1, pp. 1-12
[13] Pontryagin Duality and the Structure of Locally Compact Abelian Groups, London Mathematical Society Lecture Notes Series, vol. 29, Cambridge University Press, Cambridge–New York–Melbourne, 1977
[14] Introduction to Probability and Measure, The MacMillan Co. of India, Delhi, 1977
[15] Conditional Measures and Applications, Monographs and Textbooks in Pure and Applied Mathematics, vol. 177, Marcel Dekker Inc., New York, 1993
Cité par Sources :
