Geodesic
Asymptotic properties of some classes of generalized functions
Izvestiya. Mathematics, Tome 26 (1986) no. 1, pp. 77-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Cesáro convergence (with respect to a self-similar weight) of the Fourier–Stieltjes series of nonnegative measures. Bibliography: 13 titles. 
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Yu. N. Drozhzhinov; B. I. Zavialov. Asymptotic properties of some classes of generalized functions. Izvestiya. Mathematics, Tome 26 (1986) no. 1, pp. 77-131. http://geodesic.mathdoc.fr/item/IM2_1986_26_1_a3/

[1] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[2] Drozhzhinov Yu. N., Zavyalov B. I., “Tauberovy teoremy dlya obobschennykh funktsii s nositelyami v konusakh”, Matem. sb., 108(150):1 (1979), 78–90 | MR | Zbl

[3] Drozhzhinov Yu. N., Zavyalov B. I., “Kvaziasimptotika obobschennykh funktsii i tauberovy teoremy v kompleksnoi oblasti”, Matem. sb., 102(144):3 (1977), 372–390 | MR | Zbl

[4] Seneta E., “Regulary varying functions”, Lecture Notes in Math., 508, Springer-Verlag, N. Y., 1976 | MR | Zbl

[5] Loomis L., “The converse of the Fatou theorem for Positiv Harmonic functions”, Trans. of the Amer. Math. Soc., 53 (1943), 239–250 | DOI | MR | Zbl

[6] Drozhzhinov Yu. N., “Mnogomernaya tauberova teorema dlya golomorfnykh funktsii ogranichennogo argumenta i kvaziasimptotika passivnykh sistem”, Matem. sb., 117(159):1 (1982), 44–59 | MR | Zbl

[7] Schwartz L., Theorie des distributions. II, Hermann, Paris, 1951 | MR | Zbl

[8] Zavyalov B. I., “B'erkenovskaya asimptotika formfaktorov gluboko neuprugogo rasseyaniya i obschie printsipy teorii polya”, TMF, 33:3 (1977), 310–318 | MR

[9] Lojasiewicz S., “Sur la valeur et limite d'une distribution dans une point”, Studia Math., 16:1 (1957), 1–36 | MR | Zbl

[10] Zigmund A., Trigonometricheskie ryady, OGIZ, M., 1939

[11] Kostyuchenko A. G., Sargsyan I. S., Raspredelenie sobstvennykh znachenii, Nauka, M., 1979 | MR | Zbl

[12] Khardi G., Raskhodyaschiesya ryady, IL, M., 1951

[13] Karamata J., “Sur un mode de croissance reguliere des fonctions”, Mathematica (Cluj), 4 (1930), 38–53 | Zbl