Spectral synthesis and local description for several variables
Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 729-755.

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The problem of spectral synthesis for subspaces of analytic functions invariant under the operators of partial differentiation is reduced to the problem of the local description of closed submodules in the module of entire functions of exponential type over the ring of polynomials.
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I. F. Krasichkov-Ternovskii. Spectral synthesis and local description for several variables. Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 729-755. http://geodesic.mathdoc.fr/item/IM2_1999_63_4_a5/

[1] Schwartz L., “Theorie générale des fonctions moyenne – périodique”, Ann. of Math., 48 (1947), 857–928 | DOI | MR

[2] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. I: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 87:4 (1972), 459–489 | MR

[3] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. II: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 88:1 (1972), 3–30

[4] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. III: O rasprostranenii spektralnogo sinteza”, Matem. sb., 88:3 (1972), 331–352 | MR

[5] Krasichkov-Ternovskii I. F., “Spektralnyi sintez na sistemakh vypuklykh oblastei”, Matem. sb., 111:1 (1980), 3–41 | MR

[6] Krasichkov-Ternovskii I. F., “Spektralnyi sintez na sistemakh vypuklykh oblastei. Rasprostranenie sinteza”, Matem. sb., 112:1 (1980), 94–114 | MR

[7] Krasichkov-Ternovskii I. F., “Spektralnyi sintez na sistemakh neogranichennykh vypuklykh oblastei”, Matem. sb., 111:3 (1980), 384–401 | MR

[8] Krasichkov-Ternovskiǐ I. F., “Spectral synthesis on a system of unbounded domains starlike in a common direction”, Analysis Mathematica, 19:3 (1993), 217–223 | DOI | MR

[9] Merzlyakov S. G., “Spektralnyi sintez dlya operatora differentsirovaniya na sistemakh krivolineinykh polos”, Matem. sb., 186:5 (1995), 85–102 | MR | Zbl

[10] Merzlyakov S. G., “Invariantnye podprostranstva operatora kratnogo differentsirovaniya”, Matem. zametki, 23:5 (1982), 701–713 | MR

[11] Merzlyakov S. G., “O podprostranstvakh analiticheskikh funktsii, invariantnykh otnositelno operatora kratnogo differentsirovaniya”, Matem. zametki, 40:5 (1986), 635–639 | MR | Zbl

[12] Krasichkov-Ternovskii I. F., Shishkin A. B., “Spektralnyi sintez dlya operatora kratnogo differentsirovaniya”, DAN SSSR, 307:1 (1989), 24–27 | MR

[13] Shishkin A. B., “Spektralnyi sintez dlya operatora, porozhdennogo umnozheniem na stepen nezavisimoi peremennoi”, Matem. sb., 182:6 (1991), 828–848

[14] Krasichkov-Ternovskii I. F., “Spektralnyi sintez v kompleksnoi oblasti dlya differentsialnogo operatora s postoyannymi koeffitsientami. I: Teorema dvoistvennosti”, Matem. sb., 182:11 (1991), 1559–1587 | MR

[15] Krasichkov-Ternovskii I. F., “Spektralnyi sintez v kompleksnoi oblasti dlya differentsialnogo operatora s postoyannymi koeffitsientami. II: Metod modulei”, Matem. sb., 183:1 (1992), 3–19

[16] Krasichkov-Ternovskii I. F., “Spektralnyi sintez v kompleksnoi oblasti dlya differentsialnogo operatora s postoyannymi koeffitsientami. III: Obilnye podmoduli”, Matem. sb., 183:6 (1992), 55–86 | MR

[17] Krasichkov-Ternovskii I. F., “Spektralnyi sintez v kompleksnoi oblasti dlya differentsialnogo operatora s postoyannymi koeffitsientami. IV: Sintez”, Matem. sb., 183:8 (1992), 23–46 | MR

[18] Malgrange B., “Existence et approximation des solutions des équations aux derivées partielles et des équations de convolution”, Ann. Inst. Fourier, 6 (1955–1956), 271–355 | MR

[19] Ehrenpreis L., “Mean periodic functions”, American J. of Mathematics, 77:2 (1955), 293–328 | DOI | MR | Zbl

[20] Napalkov V. V., “Ob odnoi teoreme edinstvennosti v teorii funktsii mnogikh kompleksnykh peremennykh i odnorodnykh uravneniyakh tipa svertki v trubchatykh oblastyakh”, Izv. AN SSSR. Ser. matem., 40:1 (1971), 115–132 | MR

[21] Yulmukhametov R. S., “Odnorodnye uravneniya svertki”, DAN SSSR, 316:2 (1991), 312–315 | MR | Zbl

[22] Krivosheev A. S., Napalkov V. V., “Kompleksnyi analiz i operatory svertki”, UMN, 47:6 (1992), 3–58 | MR | Zbl

[23] Ehrenpreis L., Fourier analysis in several complex variables, Wiley Interscience Publishers, N. Y. – London, 1970 | MR | Zbl

[24] Palamodov V. P., Lineinye differentsialnye operatory s postoyannymi koeffitsientami, Nauka, M., 1967 | MR

[25] Berenstein C. A., Taylor B. A., “Interpolation problems in $\mathbb C^{@,n}$ with applications to harmonic analysis”, J. D'analyse mathematique, 38 (1980), 188–254 | MR | Zbl

[26] Struppa D. C., “The fundamental principle for systems of convolution equations”, Memoirs of the Amer. Math. Soc., 1983, no. 273 | MR

[27] Gurevich D. I., “Kontrprimery k probleme L. Shvartsa”, Funkts. analiz i ego prilozh., 9:2 (1975), 29–35 | MR | Zbl

[28] Sebastyan-i-Silva Zh., “O nekotorykh klassakh lokalnovypuklykh prostranstv, vazhnykh v prilozheniyakh”, Matematika, 1:1 (1957), 60–67

[29] Robertson A., Robertson V., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[30] Shefer Kh., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[31] Chirka E. M., “Priblizhenie mnogochlenami na zvezdnykh podmnozhestvakh $\mathbb C^{@,n}$”, Matem. zametki, 14:1 (1973), 55–60 | Zbl

[32] Ganning R., Rossi Kh., Analiticheskie funktsii mnogikh kompleksnykh peremennykh, Mir, M., 1969 | MR

[33] Shafarevich I. R., Osnovy algebraicheskoi geometrii, T. II, Nauka, M., 1988 | MR

[34] Chirka E. M., Kompleksnye analiticheskie mnozhestva, Nauka, M., 1985 | MR

[35] Trev Zh., Lektsii po lineinym uravneniyam v chastnykh proizvodnykh s postoyannymi koeffitsientami, Mir, M., 1965 | Zbl

[36] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR

[37] Dedonne Zh., Shvarts L., “Dvoistvennost v prostranstvakh $(F)$ i $(LF)$”, Matematika, 2:2 (1958), 77–102

[38] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz v normirovannykh prostranstvakh, Gos. izd-vo fiz.-mat. literatury, M., 1959 | MR

[39] Shishkin A. B., “Spektralnyi sintez dlya sistem differentsialnykh operatorov s postoyannymi koeffitsientami. Teorema dvoistvennosti”, Matem. sb., 189:9 (1998), 143–160 | MR | Zbl