Geodesic
Recovery of a~function from its coefficients in a~Dirichlet series
Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 131-159.

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

A Dirichlet series is associated, through formulas giving its coefficients, with a function analytic in a closed bounded convex domain. It is shown how to recover the function from the coefficients of the associated Dirichlet series. 
@article{IM2_1971_5_1_a8,
     author = {A. F. Leont'ev},
     title = {Recovery of a~function from its coefficients in {a~Dirichlet} series},
     journal = {Izvestiya. Mathematics },
     pages = {131--159},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a8/}
}
TY  - JOUR
AU  - A. F. Leont'ev
TI  - Recovery of a~function from its coefficients in a~Dirichlet series
JO  - Izvestiya. Mathematics 
PY  - 1971
SP  - 131
EP  - 159
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a8/
LA  - en
ID  - IM2_1971_5_1_a8
ER  - 
%0 Journal Article
%A A. F. Leont'ev
%T Recovery of a~function from its coefficients in a~Dirichlet series
%J Izvestiya. Mathematics 
%D 1971
%P 131-159
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a8/
%G en
%F IM2_1971_5_1_a8
A. F. Leont'ev. Recovery of a~function from its coefficients in a~Dirichlet series. Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 131-159. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a8/

[1] Leontev A. F., “Ob odnom svoistve edinstvennosti”, Matem. sb., 72(114) (1967), 237–250 | MR

[2] Leontev A. F., “Ob asimptotike koeffitsientov razlozheniya proizvolnykh funktsii v ryady Dirikhle”, Dokl. nauchno-tekhn. konferentsii, sektsiya matem., Mosk. energetich. in-t, 1967, 3–11 | MR

[3] Leontev A. F., “O predstavlenii proizvolnykh funktsii ryadami Dirikhle”, Dokl. AN SSSR, 164:1 (1965), 40–42 | MR

[4] Leontev A. F., “O summirovanii ryada Dirikhle s deistvitelnymi pokazatelyami dlya proizvolnoi analiticheskoi funktsii”, Izv. AN SSSR. Ser. matem., 31:1 (1967), 87–102 | MR | Zbl

[5] Bernstein V., Lecons sur les progres recents de la theorie series de Dirichlet, Paris, 1933

[6] Boas R. P., Ir., Entire functions, New York, 1954 | MR

[7] Mandeltbroit S., Kvazianaliticheskie klassy funktsii, M., L., 1937

[8] Cartwright M. L., “On integral functions of integral order”, Proc. London Math. Soc.(2), 33 (1932), 209–224 | DOI