Cite this article as:

Shishkin A. B. Projective and injective descriptions in the complex domain. Duality . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 1, pp. 47-65. DOI: https://doi.org/10.18500/1816-9791-2014-14-1-47-65


Language: 
Russian
Heading: 
UDC: 
517.5

Projective and injective descriptions in the complex domain. Duality

Abstract: 

Research of a invariant subspaces of a differential operators infinite order in a complex domain generated many issues, related with transition to dual problems. This work devoted overcome these difficulties 

References
1. Rellich F. Spektraltheorie in nichtseparablen R ¨ aumen.
Math. Ann., 1934, vol. 110, pp. 342–356.
2. Schwartz L. Th ´ eorie g ´ en ´ erale des fonctions moyennep ´ eriodiques. Ann. of Math. (2), 1947, vol. 48, pp. 857–929.
3. Tkachenko V. A. Spectral theory in spaces of analytic
functionals for operators generated by multiplication bythe independent variable. Mathematics of the USSRSbornik, 1981, vol. 40, no. 3, pp. 387–427.
4. Merzlyakov S. G., Invariant subspaces of the operator
of multiple differentiation. Mathematical Notes, 1983,vol. 33, no. 5, pp. 701—713.
5. Shishkin A. B. Spectral synthesis for an operator
generated by multiplication by a power of the independent
variable. Mathematics of the USSR-Sbornik, 1992,vol. 73, no. 1, pp. 211–229.
6. Krasichkov-Ternovskii I. F. Spectral synthesis in a
complex domain for a differential operator with constant
coefficients. I : A duality theorem. Mathematics of the
USSR-Sbornik, 1993, vol. 74, no. 2, pp. 309–335.
7. Shishkin A. B. Spectral synthesis for systems
of differential operators with constant coefficients.
Mathematics of the USSR-Sbornik, 2003, vol. 194, no. 12,pp. 1865–1898.
8. Shishkin A. B. Spectral synthesis for systems of
differential operators with constant coefficients. Duality
theorem. Mathematics of the USSR-Sbornik, 1998,
vol. 189, no. 9, pp. 1423–1440.
9. Chernyshev A. N. Spectral synthesis for infinitely
differential operator with constant coefficients. Duality
theorem. Trudi FORA, 2001, vol. 6, pp. 75–87 (in Russian).
10. Edwards R. E. Functional Analysis. Theory and
Applications. New York, Holt, Rinehart and Winston,1965.
11. Gunning R. C., Rossi H. Analytic functions of several64 Научный отдел
В. А. Юрко. Об обратной задаче для дифференциальных операторов на графе-ежеcomplex variables. Prentice-Hall, Inc., Englewood Cliffs,
N.J., 1965, 317 p. (Rus. ed. : Gunning R., Rossi Kh. Analiticheskie funktsii mnogikh kompleksnykhperemennykh. Moscow, Mir, 1969, 395 p.)
12. Hermander L. An introduction to the theory offunctions of several complex variables (Rus. ed. :
Hermander L. Vvedenie v teoriyu funktsii neskol’kikh kompleksnykh peremennykh. Moscow, Mir, 1968, 279 p.)
13. Krasichkov-Ternovskii I. F. Local description of closed ideals and submodules of analytic functions of one
variable. II. Mathematics of the USSR-Izvestiya, 1980, vol. 14, no. 2, pp. 289–316
Full text: