Geodesic
Tangential boundary values of Laplace transforms. Applications to Muntz--Szasz type approximation
Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 161-181.

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We consider the Laplace transforms (LT) of functions in $L^q(\mathbb R_+)$, $1$, with a slowly varying weight. We prove that if the weight satisfies certain conditions, then each LT of this class has tangential boundary values almost everywhere on the imaginary axis, and the structure of the corresponding neighbourhoods depends on the weight only. This result is applied to distinguish a wide class of weighted $L^p$ spaces on the half-line such that the Szasz condition is not necessary for the completeness of the system $\exp(-\lambda_n t)$ in these spaces. 
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A. M. Sedletskii. Tangential boundary values of Laplace transforms. Applications to Muntz--Szasz type approximation. Izvestiya. Mathematics , Tome 67 (2003) no. 1, pp. 161-181. http://geodesic.mathdoc.fr/item/IM2_2003_67_1_a8/

[1] Nevanlinna R., Odnoznachnye analiticheskie funktsii, GITTL, M., 1941

[2] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M., 1950

[3] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR

[4] Kinney J. R., “Tangential limits of functions of the class $S_\alpha$”, Proc. Amer. Math. Soc., 14 (1963), 68–70 | DOI | MR | Zbl

[5] Cruzeiro A. B., “Convergence quasi partout dans des domaines paraboliques des fonctions d'intègrale de Dirichlet finie”, C. R. Acad. Sci. Paris. Sér. I, 294 (1982), 13–16 | MR | Zbl

[6] Nagel A., Rudin W., Shapiro J. H., “Tangential boundary behavior of function in Dirichlet-type spaces”, Ann. Math., 116 (1982), 331–360 | DOI | MR | Zbl

[7] Krotov V. G., “O kasatelnom granichnom povedenii funktsii mnogikh peremennykh”, Matem. zametki, 68:2 (2000), 230–248 | MR | Zbl

[8] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | MR | Zbl

[9] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[10] Goldberg A. A., Ostrovskii I. V., Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR

[11] Sedletskii A. M., “O ravnomernoi skhodimosti negarmonicheskikh ryadov Fure”, Tr. MIAN, 200, Nauka, M., 1991, 299–309

[12] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[13] Müntz Ch., “Über den Approximationssatz von Weierstrass”, H. A. Schwartz Festschrift, Berlin, 1914, 303–312

[14] Szász O., “Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen”, Math. Ann., 77 (1916), 482–496 | DOI | MR | Zbl

[15] Schwartz L., Étude des sommes d'exponentielles, Hermann, Paris, 1959 | MR

[16] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[17] Grum M., “On the theorems of Müntz and Szász”, J. London Math. Soc., 31 (1956), 433–437 | DOI | MR

[18] Grum M., “On the theorems of Müntz and Szász. Corrigendum and addendum”, J. London Math. Soc., 32 (1957), 517

[19] Siegel A., “On the Müntz–Szász theorem for $C[0,1]$”, Proc. Amer. Math. Soc., 36 (1972), 161–166 | DOI | MR | Zbl

[20] Sedletskii A. M., “Problema Myuntsa–Sasa i nuli analiticheskikh funktsii”, Tr. 3-ei Sarat. zim. shk. “Teor. funkts. i priblizh.”, Ch. 1 (27 yanv.–7 fevr. 1986 g.), Saratov, 1987, 59–63 | MR

[21] Sedletskii A. M., “O polnote sistem eksponent na polupryamoi”, Matem. zametki, 48:5 (1990), 88–96 | MR

[22] Sedletskii A. M., Fourier transforms and approximations, Gordon and Breach Science Publishers, Amsterdam, 2000 | MR | Zbl