Geodesic
Entire functions of sine type and their applications
Algebra i analiz, Tome 22 (2010) no. 5, pp. 49-68.

Voir la notice de l'article provenant de la source Math-Net.Ru

For subharmonic functions that depend only on the real part of $z$, new constructions of “sine type functions” are presented. This term is reserved for entire functions whose deviation from a given function is majorized, everywhere except some collection of disks, by a certain constant. It is shown that the system of exponentials constructed by the zeros of a sine type function for some convex function is complete and minimal in a certain weighted Hilbert space on an interval of the real line.
Keywords: entire functions, Hilbert spaces, completeness and minimality for a system of exponentials, Fourier–Laplace transformation. 
@article{AA_2010_22_5_a1,
     author = {R. A. Bashmakov and A. A. Putintseva and R. C. Yulmukhametov},
     title = {Entire functions of sine type and their applications},
     journal = {Algebra i analiz},
     pages = {49--68},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2010_22_5_a1/}
}
TY  - JOUR
AU  - R. A. Bashmakov
AU  - A. A. Putintseva
AU  - R. C. Yulmukhametov
TI  - Entire functions of sine type and their applications
JO  - Algebra i analiz
PY  - 2010
SP  - 49
EP  - 68
VL  - 22
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2010_22_5_a1/
LA  - ru
ID  - AA_2010_22_5_a1
ER  - 
%0 Journal Article
%A R. A. Bashmakov
%A A. A. Putintseva
%A R. C. Yulmukhametov
%T Entire functions of sine type and their applications
%J Algebra i analiz
%D 2010
%P 49-68
%V 22
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2010_22_5_a1/
%G ru
%F AA_2010_22_5_a1
R. A. Bashmakov; A. A. Putintseva; R. C. Yulmukhametov. Entire functions of sine type and their applications. Algebra i analiz, Tome 22 (2010) no. 5, pp. 49-68. http://geodesic.mathdoc.fr/item/AA_2010_22_5_a1/

[1] Levin B. Ya., Lyubarskii Yu. I., “Interpolyatsiya tselymi funktsiyami spetsialnykh klassov i svyazannye s neyu razlozheniya v ryady eksponent”, Izv. AN SSSR. Ser. mat., 39:3 (1975), 657–702 | MR | Zbl

[2] Azarin V. S., “O luchakh vpolne regulyarnogo rosta tseloi funktsii”, Mat. sb., 79:4 (1969), 463–476 | MR | Zbl

[3] Yulmukhametov R. S., “Approksimatsiya subgarmonicheskikh funktsii”, Anal. Math., 11 (1985), 257–282 | DOI | MR | Zbl

[4] Lyubarskii Yu. I., Sodin M. L., Analogi funktsii tipa sinusa dlya vypuklykh oblastei, Preprint No 17, Fiz.-tekhn. in-t nizkikh temperatur AN USSR, Kharkov, 1986

[5] Leontev A. F., Tselye funktsii. Ryady eksponent, Nauka, M., 1983 | MR

[6] Lutsenko V. I., Yulmukhametov R. S., “Obobschenie teoremy Peli–Vinera na vesovye prostranstva”, Mat. zametki, 48:5 (1990), 80–87 | MR | Zbl

[7] Chyzhikov I. E., “Approximation of subharmonic functions of slow growth”, Mat. Fiz. Anal. Geom., 9:3 (2002), 509–520 | MR

[8] Isaev K. P., Putintseva A. A., Yulmukhametov R. S., “Predstavlenie ryadami eksponent v vesovykh prostranstvakh na veschestvennoi osi”, Ufimskii mat. zh., 1:1 (2009), 16–37

[9] Levin B. Ya., “O bazisakh pokazatelnykh funktsii v $L^2(-\pi,\pi)$”, Zap. fiz.-mat. fak. Kharkov. gos. un-ta i Kharkov. mat. o-va, 27:4 (1961), 39–48

[10] Lyubarskii Yu., Malinnikova E., “On approximation of subharmonic functions”, J. Anal. Math., 83 (2001), 121–149 | DOI | MR | Zbl