The general form of isomorphisms commuting with differentiation in spaces of entire functions of slow growth
Sbornik. Mathematics, Tome 20 (1973) no. 4, pp. 493-505 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The general form is found for an isomorphism $I$ in a space of entire functions of several complex variables of sufficiently slow growth, when $I$ is required to commute with every operator $D^p=\partial^{p_1+\dots+p_n}/\partial z^{p_1}_1\cdots\partial z^{p_n}_n$. Bibliography: 14 titles.
@article{SM_1973_20_4_a0,
     author = {Yu. F. Korobeinik and V. V. Morzhakov},
     title = {The general form of isomorphisms commuting with differentiation in spaces of entire functions of slow growth},
     journal = {Sbornik. Mathematics},
     pages = {493--505},
     year = {1973},
     volume = {20},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_20_4_a0/}
}
TY  - JOUR
AU  - Yu. F. Korobeinik
AU  - V. V. Morzhakov
TI  - The general form of isomorphisms commuting with differentiation in spaces of entire functions of slow growth
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 493
EP  - 505
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1973_20_4_a0/
LA  - en
ID  - SM_1973_20_4_a0
ER  - 
%0 Journal Article
%A Yu. F. Korobeinik
%A V. V. Morzhakov
%T The general form of isomorphisms commuting with differentiation in spaces of entire functions of slow growth
%J Sbornik. Mathematics
%D 1973
%P 493-505
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1973_20_4_a0/
%G en
%F SM_1973_20_4_a0
Yu. F. Korobeinik; V. V. Morzhakov. The general form of isomorphisms commuting with differentiation in spaces of entire functions of slow growth. Sbornik. Mathematics, Tome 20 (1973) no. 4, pp. 493-505. http://geodesic.mathdoc.fr/item/SM_1973_20_4_a0/

[1] J. Delsartes, J. L. Lions, “Transmutations d'operateurs différentielles dan le domaine complexe”, Comm. Math. Helv., 32 (1957), 113–128 | DOI | MR

[2] I. Ya. Viner, “Preobrazovanie differentsialnykh operatorov v prostranstvakh golomorfnykh funktsii”, Uspekhi matem. nauk, XX:1 (121) (1965), 185–188 | MR

[3] N. I. Nagnibida, “K voprosu ob izomorfizmakh analiticheskogo prostranstva, perestanovochnykh so stepenyu operatora differentsirovaniya”, DAN SSSR, 167:6 (1966), 1230–1233 | MR | Zbl

[4] A. Martineau, “Équations différentielles d'ordre infini”, Bull. Soc. math. France, 95 (1968), 109–154 | MR

[5] B. Malgrange, “Existence et approximation des solutions des équations aux derivées partielles et des équations de convolution”, Ann. Inst. Fourier, 6 (1955), 271–354 | MR

[6] R. Edvards, Funktsionalnyi analiz (teoriya i prilozheniya), izd-vo «Mir», Moskva, 1969

[7] Yu. F. Korobeinik, “O nekotorykh kharakteristicheskikh svoistvakh operatorov beskonechnogo poryadka”, Izv. AN SSSR, seriya matem., 30:5 (1966), 993–1016 | MR | Zbl

[8] Yu. F. Korobeinik, “Obschii vid lineinogo funktsionala v nekotorykh prostranstvakh analiticheskikh funktsii i ego prilozheniya v teorii differentsialnykh operatorov beskonechnogo poryadka”, Matem. analiz i ego prilozheniya, izd. RGU, Rostov-na-Donu, 1969, 116–132 | MR

[9] V. V. Morzhakov, “K teorii primenimosti differentsialnykh operatorov beskonechnogo poryadka v prostranstvakh funktsii mnogikh kompleksnykh peremennykh”, Litovskii matem. sb., 11 (1971), 843–859 | Zbl

[10] A. V. Kantorovich, V. I. Krylov, Priblizhennye metody vysshego analiza, Gostekhizdat, Leningrad–Moskva, 1949

[11] Iv. Raichinov, “V'erkhu edna klasa lineini operatori”, God. minno-geol. in-t, 9, Sofiya, 1962–1963, 425–430

[12] R. P. Boas, “Functions of exponential type, III”, Duke. Math. J., 2 (1944), 507–511 | DOI | MR | Zbl

[13] D. Djoković, “A remark on the paper of Iv. Raitchinov sur une théorème de G. Polya”, Publ. Inst. Math., 3 (1963), 41–42 | MR | Zbl

[14] S. Rolewicz, “On Cauchy - Hadamard formula for Köethe power series”, Bull. Acad. Polon. sci., X:4 (1962), 211–216 | MR