[Sur le théorème de Lévy–Raikov–Marcinkiewicz]
Let μ be a finite nonnegative Borel measure. The classical Lévy–Raikov–Marcinkiewicz theorem states that if its Fourier transform
Soit une mesure de Borel μ, finie et non-négative. Le théorème classique de Lévy–Raikov–Marcinkiewicz affirme que la transformée de Fourier
Accepté le :
Publié le :
Iossif Ostrovskii 1, 2 ; Alexander Ulanovskii 3
@article{CRMATH_2003__336_3_237_0, author = {Iossif Ostrovskii and Alexander Ulanovskii}, title = {On the {L\'evy{\textendash}Raikov{\textendash}Marcinkiewicz} theorem}, journal = {Comptes Rendus. Math\'ematique}, pages = {237--240}, publisher = {Elsevier}, volume = {336}, number = {3}, year = {2003}, doi = {10.1016/S1631-073X(03)00035-9}, language = {en}, }
Iossif Ostrovskii; Alexander Ulanovskii. On the Lévy–Raikov–Marcinkiewicz theorem. Comptes Rendus. Mathématique, Volume 336 (2003) no. 3, pp. 237-240. doi : 10.1016/S1631-073X(03)00035-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00035-9/
[1] The Analysis of Linear Partial Differential Operators, I, Springer-Verlag, Berlin, 1983
[2] Decomposition of Random Variables and Vectors, American Mathematical Society, Providence, RI, 1977
[3] On sign changes of distributions having spectral gap at the origin, C. R. Acad. Sci. Paris, Sér. I, Volume 336 (2003) (to be published)
- Oscillation of Fourier integrals with a spectral gap, Journal de Mathématiques Pures et Appliquées, Volume 83 (2004) no. 3, p. 313 | DOI:10.1016/s0021-7824(03)00064-3
- On the Lévy–Raikov–Marcinkiewicz theorem, Journal of Mathematical Analysis and Applications, Volume 296 (2004) no. 1, p. 314 | DOI:10.1016/j.jmaa.2004.04.021
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