Intégrales trigonométriques et pseudofonctions
González Vieli, Francisco Javier
Annales de l'Institut Fourier, Tome 44 (1994), p. 197-211 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

On étudie un analogue à plusieurs variables réelles de la théorie de Riemann des séries trigonométriques vue sous l’angle des pseudofonctions, en utilisant le laplacien intégral et la fonction de Riemann qui découle de ce choix.

An analogue in several real variables of Riemann’s theory on trigonometric series is studied, with emphasis on pseudofunctions and using the integral laplacian and the Riemann’s function which follows from this choice.

@article{AIF_1994__44_1_197_0,
     author = {Gonz\'alez Vieli, Francisco Javier},
     title = {Int\'egrales trigonom\'etriques et pseudofonctions},
     journal = {Annales de l'Institut Fourier},
     volume = {44},
     year = {1994},
     pages = {197-211},
     doi = {10.5802/aif.1394},
     mrnumber = {95a:42021},
     zbl = {0791.42010},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1994__44_1_197_0}
}

González Vieli, Francisco Javier. Intégrales trigonométriques et pseudofonctions. Annales de l'Institut Fourier, Tome 44 (1994) pp. 197-211. doi : 10.5802/aif.1394. http://gdmltest.u-ga.fr/item/AIF_1994__44_1_197_0/

[AW]J.M. Ash and G.V. Welland, Convergence, uniqueness and summability of multiple trigonometric series, Trans. Amer. Math. Soc., 163 (1972), 401-436. | MR 45 #9057 | Zbl 0233.42014

[Ba]N.K. Bary, A Treatise on Trigonometric Series, Pergamon Press, Oxford, 1964. | MR 30 #1347 | Zbl 0129.28002

[Be]J.J. Benedetto, Spectral Synthesis, B.G. Teubner, Stuttgart, 1975. | Zbl 0364.43001

[CS]A. Carbery and F. Soria, Almost-Everywhere Convergence of Fourier Integrals [...], Revista Matemȥtica Iberoamericana, vol. 4, n°2 (1988), 319-337. | Zbl 0692.42001

[D]N.F. Donoghue, Distributions and Fourier Transforms, Academic Press, New York, 1969. | Zbl 0188.18102

[KS]J.-P. Kahane et R. Salem, Ensembles parfaits et séries trigonométriques, Hermann, Paris, 1963. | MR 28 #3279 | Zbl 0112.29304

[KL]A.S. Kechris & A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, Cambridge University Press, 1987. | MR 90a:42008 | Zbl 0642.42014

[Sh]V.L. Shapiro, Fourier series in several variables, Bull. Amer. Math. Soc., 70 (1964), 48-93. | MR 28 #1448 | Zbl 0267.42011

[SW]E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971. | MR 46 #4102 | Zbl 0232.42007

[Sz]E. Szpilrajn, Remarques sur les fonctions sousharmoniques, Annals of Math., 1933 (34), 588-594. | JFM 59.0487.03 | Zbl 0007.15401

[W]G.N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, 1922. | JFM 50.0264.01

[Z]A. Zygmund, Trigonometric Series, Cambridge University Press, 1977.