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
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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
@article{INTO_2018_153_a9,
     author = {I. Kh. Musin},
     title = {On {A} {Certain} {Class} of {Entire} {Functions}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {135--142},
     year = {2018},
     volume = {153},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_153_a9/}
}
TY  - JOUR
AU  - I. Kh. Musin
TI  - On A Certain Class of Entire Functions
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 135
EP  - 142
VL  - 153
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_153_a9/
LA  - ru
ID  - INTO_2018_153_a9
ER  - 
%0 Journal Article
%A I. Kh. Musin
%T On A Certain Class of Entire Functions
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 135-142
%V 153
%U http://geodesic.mathdoc.fr/item/INTO_2018_153_a9/
%G ru
%F INTO_2018_153_a9
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