On A Certain Class of Entire Functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 135-142.

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In this paper, we examine the problem on the description in terms of the Laplace transform of functionals from the conjugate space for the Hilbert space of entire functions of $n$ variables constructed by a convex function in ${\mathbb C}^n$, which depends on the modules of variables and grows at infinity faster than $a\|z\|$ for any $a>0$.
Keywords: Hilbert space, entire function, convex function, Young–Fenchel transform.
Mots-clés : Laplace transform
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I. Kh. Musin. On A Certain Class of Entire Functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 135-142. http://geodesic.mathdoc.fr/item/INTO_2018_153_a9/

[1] Bashmakov R. A., Isaev K. P., Yulmukhametov R. S., “O geometricheskikh kharakteristikakh vypuklykh funktsii i integralax Laplasa”, Ufim. mat. zh., 2:1 (2010), 3–16 | MR | Zbl

[2] Napalkov V. V., Bashmakov R. A., Yulmukhametov R. S., “Asimptoticheskoe povedenie integralov Laplasa i geometricheskie kharakteristiki vypuklykh funktsii”, Dokl. RAN, 413:1 (2007), 20–22 | Zbl

[3] Napalkov V. V., Popenov S. V., “O preobrazovanii Laplasa funktsionalov v vesovom prostranstve Bergmana tselykh funktsii v ${\mathbb C}^n$”, Dokl. RAN, 352:5 (1997), 595–597 | MR | Zbl

[4] Napalkov V. V., Yulmukhametov R. S., “Vesovye preobrazovaniya Fure—Laplasa analiticheskikh funktsionalov v kruge”, Mat. sb., 183:11 (1992), 139–144 | Zbl

[5] Popenov S. V., “O preobrazovanii Laplasa funktsionalov v nekotorykh vesovykh prostranstvakh Bergmana v ${\mathbb C}^n$”, Kompleksnyi analiz, differentsialnye uravneniya, chislennye metody i prilozheniya, v. 2, Kompleksnyi analiz, Ufa, 1996, 125–132

[6] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. II, Nauka, M., 1970

[7] Yulmukhametov R. S., “Asimptotika mnogomernogo integrala Laplasa”, Issledovaniya po teorii priblizhenii, Ufa, 1989, 132–137 | MR | Zbl

[8] Azagra D., “Global and fine approximation of convex functions”, Proc. London Math. Soc., 107:4 (2013), 799–824 | DOI | MR | Zbl

[9] Azagra D., Global approximation of convex functions, arXiv: 1112.1042 [math.FA]

[10] Musin I. Kh., “On a space of entire functions rapidly decreasing on $R^n$ and its Fourier transform”, Concr. Oper., 2:1 (2015), 120–138 | MR | Zbl

[11] Taylor B. A., “On weighted polynomial approximation of entire functions”, Pac. J. Math., 36:2 (1971), 523–539 | DOI | MR