Geodesic
Estimates of the growth and decrease on curves of an entire function
Sbornik. Mathematics, Tome 194 (2003) no. 8, pp. 1167-1194 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Relations between the growth of an entire Dirichlet series with Fejér lacunae and its decrease on curves going to infinity are studied. Sharp estimates are found in the most general case. 
@article{SM_2003_194_8_a3,
     author = {A. M. Gaisin},
     title = {Estimates of the growth and decrease on curves of an~entire function},
     journal = {Sbornik. Mathematics},
     pages = {1167--1194},
     year = {2003},
     volume = {194},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_8_a3/}
}
TY  - JOUR
AU  - A. M. Gaisin
TI  - Estimates of the growth and decrease on curves of an entire function
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 1167
EP  - 1194
VL  - 194
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_8_a3/
LA  - en
ID  - SM_2003_194_8_a3
ER  - 
%0 Journal Article
%A A. M. Gaisin
%T Estimates of the growth and decrease on curves of an entire function
%J Sbornik. Mathematics
%D 2003
%P 1167-1194
%V 194
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2003_194_8_a3/
%G en
%F SM_2003_194_8_a3
A. M. Gaisin. Estimates of the growth and decrease on curves of an entire function. Sbornik. Mathematics, Tome 194 (2003) no. 8, pp. 1167-1194. http://geodesic.mathdoc.fr/item/SM_2003_194_8_a3/

[1] Fejér L., “Über die Wurzel vom kleinsten absoluten Betrage einer algebraischen Gleichung”, Math. Ann., 1908, 413–423 | DOI | MR | Zbl

[2] Macintyre A. J., “Asymptotic paths of integral functions with gap power series”, Proc. London Math. Soc. (3), 2:2 (1952), 286–296 | DOI | MR | Zbl

[3] Pólya G., “Untersuchungen über Lücken und Singularitäten von Potenzeihen”, Math. Z., 29 (1929), 549–640 | DOI | MR | Zbl

[4] Fuchs W. H. J., “Proof of a conjecture of G. Pólya concerning gap series”, Illinois J. Math., 7 (1963), 661–667 | MR | Zbl

[5] Kövari T., “A gap-theorem for entire functions of infinite order”, Michigan Math. J., 12:2 (1965), 133–140 | DOI | MR | Zbl

[6] Kövari T., “On the asymptotic paths of entire functions with gap power series”, J. Anal. Math., 15 (1965), 281–286 | DOI | MR | Zbl

[7] Sons L. R., “On the Macintyre conjecture”, Illinois J. Math., 14 (1970), 613–629 | MR

[8] Sons L. R., “An analogue of a theorem of W. H. J. Fuchs on gap series”, Proc. London Math. Soc. (3), 21:3 (1970), 525–539 | DOI | MR | Zbl

[9] Hayman W. K., “Angular value distribution of power series with gaps”, Proc. London Math. Soc. (3), 24 (1972), 590–624 | DOI | MR | Zbl

[10] Pavlov A. I., “O roste po krivym tselykh funktsii, zadannykh lakunarnymi stepennymi ryadami”, Sib. matem. zhurn., 13:5 (1972), 1169–1181 | MR | Zbl

[11] Pavlov A. I., “O roste na polozhitelnom luche tselykh funktsii s veschestvennymi koeffitsientami Teilora”, Matem. zametki, 14:4 (1973), 577–588 | MR | Zbl

[12] Korevaar J., Dixon M., “Interpolation, strongly nonspanning powers and Macintyre exponents”, Indag. Math. (N.S.), 40:2 (1978), 243–258 | MR

[13] Berndtsson B., “A note on Pavlov–Korevaar–Dixon interpolation”, Indag. Math. (N.S.), 81 (1978), 400–414 | MR

[14] Murai T., “The deficiency of entire functions with Fejer gaps”, Ann. Inst. Fourier (Grenoble), 33:3 (1983), 39–58 | MR | Zbl

[15] Gaisin A. M., “Asimptoticheskoe povedenie summy tselogo ryada Dirikhle na krivykh”, Issledovaniya po teorii priblizhenii, BNTs UrO AN SSSR, Ufa, 1989, 3–15 | MR | Zbl

[16] Gaisin A. M., “Usilennaya nepolnota sistemy eksponent i problema Makintaira”, Matem. sb., 182:7 (1991), 931–945 | MR | Zbl

[17] Skaskiv O. B., “On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series”, Anal. Math., 16:2 (1990), 143–157 | DOI | MR | Zbl

[18] Gaisin A. M., “Ob odnoi gipoteze Polia”, Izv. RAN. Ser. matem., 58:2 (1994), 73–92 | MR | Zbl

[19] Gaisin A. M., Asimptoticheskie svoistva funktsii, zadannykh ryadami eksponent, Dis. ... dokt. fiz.-matem. nauk, Ufa, 1994

[20] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[21] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR

[22] Gaisin A. M., “Ob odnoi teoreme Kheimana”, Sib. matem. zhurn., 39:3 (1998), 501–516 | MR | Zbl

[23] Gaisin A. M., “Asimptoticheskaya otsenka summy ryada Dirikhle na krivykh”, Matem. zametki, 61:6 (1997), 810–816 | MR | Zbl

[24] Sheremeta M. N., “Ob odnom svoistve tselykh funktsii s veschestvennymi teilorovskimi koeffitsientami”, Matem. zametki, 18:3 (1975), 395–402 | MR | Zbl

[25] Gaisin A. M., “Behavior of logarithm of modulus of the sum of Dirichlet series on curves”, J. Anal., 3 (1995), 205–211 | MR | Zbl

[26] Gaisin A. M., “Otsenka ryada Dirikhle s lakunami Feiera na krivykh”, Dokl. RAN, 370:6 (2000), 735–737 | MR | Zbl

[27] Evgrafov M. A., “Ob odnoi teoreme edinstvennosti dlya ryadov Dirikhle”, UMN, 17:3 (1962), 169–175 | MR | Zbl

[28] Sheremeta M. M., “Five open problems in the theory of entire functions”, Matematichnï studiï, 6 (1996), 157–159

[29] Beurling A., “Some theorems on boundedness of analytic functions”, Duke Math. J., 16 (1949), 355–359 | DOI | MR | Zbl

[30] Hayman W. K., “How guickly can an entire function tend to zero along curve?”, Enseign Math. (2), 24:3–4 (1978), 215–223 | MR | Zbl

[31] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR | Zbl

[32] Boichuk V. S., “O nekotorykh svoistvakh utochnennogo poryadka”, Sib. matem. zhurn., 20:2 (1979), 229–236 | MR