Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Strukov V. E. Structure of the inverse for the integral operator of special kind. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 2, pp. 22-30. DOI: 10.18500/1816-9791-2013-13-2-1-22-30, EDN: SJJAWL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
27.02.2013
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.9
DOI: 
10.18500/1816-9791-2013-13-2-1-22-30
EDN: 
SJJAWL

Structure of the inverse for the integral operator of special kind

Autors: 
Strukov Victor Evgen'evich, Voronezh State University
Abstract: 

Algebra (with identity) generated by integral operators on the spaces of continuous periodic functions is considered. This algebra is proved to be an inverse-closed subalgebra in the algebra of all bounded linear operators. 

Key words: 
Banach space
integral operator
Bochner–Phillips theorem
Fourier series of an operator
inverse-closedness of a subalgebra
Wiener's pair of algebras
References: 
  1. Naimark M. A. Normirovannye kol’tsa [Normed Rings]. Moscow, Nauka Publ., 1968, 664 p. (in Russian).
  2. Burbaki N. Spektral’naya teoriya [Spectral theory]. Moscow, Mir, 1972, 183 p. (in Russian).
  3. Bochner S., Fillips R. S. Absolutely convergent Fourier expansion for non-commutative normed rings. Ann. of Math., 1942, no. 3, pp. 409–418.
  4. Baskakov A. G. Wiener’s theorem and the asymptotic estimates of the elements of inverse matrices. Functional Analysis and Its Applications, 1990, vol. 24, no. 3, pp. 222–224.
  5. Baskakov A. G. Absteact haemonic analysis and asymptotic estimates of elements of inverse matrices. Math. Notes, 1992, vol. 52, iss. 2, pp. 764–771.
  6. Baskakov A. G. On Spectral Properties of Some Classes of Linear Operators. Functional Analysis and Its Applications, 1995, vol. 29, no. 2, pp. 121–123.
  7. Baskakov A. G. Asymptotic estimates for elements of matrices of inverse operators, and harmonic analysis. Siberian Math. J., 1997, vol. 38, iss. 1, pp. 10–22.
  8. Baskakov A. G. Estimates for the entries of inverse matrices and the spectral analysis of linear operators. Izvestiya: Mathematics, 1997, vol. 61, no. 6, pp. 1113– 1135. DOI: 10.4213/im164.
  9. Baskakov A. G. Garmonicheskii analiz lineinykh operatorov [Harmonic analysis of linear operators]. Voronezh, Voronezh Univ. Press, 1987, 165 p. (in Russian).
  10. Kurbatov V. G. Algebras of difference and integral operators. Functional Analysis and Its Applications, 1990, vol. 24, no. 2, pp. 156–158. 
  11. Strukova I. I. Wiener’s theorem for periodic at infinity functions. Izv. Sarat. Univ. N. S. Ser. Math. Mech. Inform., 2012, vol. 12, iss. 4, pp. 34–41 (in Russian). 6 Scientific
Received: 
07.09.2012
Accepted: 
09.01.2013
Published: 
27.02.2013
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