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 Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 276–308 (Mi izv1241)

Factorization of almost periodic matrix-valued functions and the Noether theory for certain classes of equations of convolution type

Yu. I. Karlovich, I. M. Spitkovsky

Abstract: The authors study $n$- and $d$-normality and compute the index of systems of singular integral equations with a semi-almost periodic matrix-valued coefficient $G$, as well as the index of operators of convolution type on the half-line and a finite interval converging to it. At the base of the investigation lies factorization with almost periodic factors of matrix-valued functions describing the asymptotics of $G$ at $\pm\infty$.
Bibliography: 38 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 281–316

Bibliographic databases:

UDC: 517.518.6+517.968.25
MSC: Primary 45E10; Secondary 35Q15, 30E25, 47A53, 42A75, 47A68
Revised: 03.08.1987

Citation: Yu. I. Karlovich, I. M. Spitkovsky, “Factorization of almost periodic matrix-valued functions and the Noether theory for certain classes of equations of convolution type”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 276–308; Math. USSR-Izv., 34:2 (1990), 281–316

Citation in format AMSBIB
\Bibitem{KarSpi89} \by Yu.~I.~Karlovich, I.~M.~Spitkovsky \paper Factorization of almost periodic matrix-valued functions and the Noether theory for certain classes of equations of convolution type \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1989 \vol 53 \issue 2 \pages 276--308 \mathnet{http://mi.mathnet.ru/izv1241} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=998297} \zmath{https://zbmath.org/?q=an:0691.45007|0681.45003} \transl \jour Math. USSR-Izv. \yr 1990 \vol 34 \issue 2 \pages 281--316 \crossref{https://doi.org/10.1070/IM1990v034n02ABEH000646} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. A. Bastos, A. F. Dos Santos, R. Duduchava, “Finite Interval Convolution Operators on the Bessel Potential Spaces Hsp”, Math Nachr, 173:1 (1995), 49
2. L.P. Castro, F.O. Speck, “A fredholm study for convolution operators with piecewise continuous symbols on a union of a finite and a semi-infinite intervel1”, Applicable Analysis, 64:1-2 (1997), 171
3. J. A. Ball, Yu. I. Karlovich, L. Rodman, I. M. Spitkovsky, “Sarason interpolation and Toeplitz corona theorem for almost periodic matrix functions”, Integr equ oper theory, 32:3 (1998), 243
4. M.A. Bastos, Yu.I. Karlovich, A.F. dos Santos, P.M. Tishin, “The Corona Theorem and the Existence of Canonical Factorization of Triangular AP-Matrix Functions”, Journal of Mathematical Analysis and Applications, 223:2 (1998), 494
5. M.A. Bastos, Yu.I. Karlovich, A.F. dos Santos, P.M. Tishin, “The Corona Theorem and the Canonical Factorization of Triangular AP Matrix Functions—Effective Criteria and Explicit Formulas”, Journal of Mathematical Analysis and Applications, 223:2 (1998), 523
6. A. Böttcher, “On the corona theorem for almost periodic functions”, Integr equ oper theory, 33:3 (1999), 253
7. L. P. Castro, F. O. Speck, “Relations between convolution type operators on intervals and on the half-line”, Integr equ oper theory, 37:2 (2000), 169
8. P. A. Lopes, A. F. Santos, “New results on the invertibility of the finite interval convolution operator”, Integr equ oper theory, 38:3 (2000), 317
9. L.P. Castro, “A relation between convolution type operators on intervals in sobolev spaces”, Applicable Analysis, 74:3-4 (2000), 393
10. M. A. Bastos, Yu. I. Karlovich, A. F. Santos, “The invertibility of convolution type operators on a union of intervals and the corona theorem”, Integr equ oper theory, 42:1 (2002), 22
11. M.A. Bastos, Yu.I. Karlovich, A.F. dos Santos, “Oscillatory Riemann–Hilbert problems and the corona theorem”, Journal of Functional Analysis, 197:2 (2003), 347
12. A. Böttcher, Yu.I. Karlovich, I.M. Spitkovsky, “The -algebra of singular integral operators with semi-almost periodic coefficients”, Journal of Functional Analysis, 204:2 (2003), 445
13. S.T. Naique, A.F. dos Santos, “Polynomial almost periodic solutions for a class of Riemann–Hilbert problems with triangular symbols”, Journal of Functional Analysis, 240:1 (2006), 226
14. M.C. Câmara, A.F. dos Santos, M.C. Martins, “A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann–Hilbert problems”, Journal of Functional Analysis, 235:2 (2006), 559
15. M.C. Câmara, Yu.I. Karlovich, I.M. Spitkovsky, “Constructive almost periodic factorization of some triangular matrix functions”, Journal of Mathematical Analysis and Applications, 367:2 (2010), 416
16. M. C. Câmara, Yu. I. Karlovich, I. M. Spitkovsky, “Kernels of Asymmetric Toeplitz Operators and Applications to Almost Periodic Factorization”, Complex Anal. Oper. Theory, 2011
17. L.P. Castro, D. Kapanadze, “Wave diffraction by a half-plane with an obstacle perpendicular to the boundary”, Journal of Differential Equations, 2012
18. L.P..  Castro, David Kapanadze, “Mixed boundary value problems of diffraction by a half-plane with an obstacle perpendicular to the boundary”, Math. Meth. Appl. Sci, 2013, n/a
19. M.C. Câmara, C. Diogo, I.M. Spitkovsky, “Toeplitz operators of finite interval type and the table method”, Journal of Mathematical Analysis and Applications, 2015