Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Shishkin A. B. Projective and injective descriptions in the complex domain. Duality. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 1, pp. 47-65. DOI: 10.18500/1816-9791-2014-14-1-47-65, EDN: SCSSRV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.03.2014
Full text:
download
(downloads: 255)
Language: 
Russian
Heading: 
Mathematics
UDC: 
517.5
DOI: 
10.18500/1816-9791-2014-14-1-47-65
EDN: 
SCSSRV

Projective and injective descriptions in the complex domain. Duality

Autors: 
Shishkin Andrei Borisovich, Kuban State University
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 

Key words: 
nvariant subspaces
spectral synthesis
local description
projective description
injective description
duality
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
Received: 
19.08.2013
Accepted: 
21.01.2014
Published: 
28.02.2014
  • 1129 reads