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On explicit factorization and applications

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This paper is devoted to two topics connected with factorization of triangular 2 by 2 matrix functions. The first application is concerned with explicit factorization of a class of matrices of Daniel-Khrapkov type and the second is related to inversion of finite Toeplitz matrices. In the first section we present the scheme of factorization of triangular 2 by 2 matrix functions.

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References

  • [Ch] Chebotarev, G.N.,Partial indices for the Riemann boundary problem for a triangular matrix of second order, Uspehi Mat. Nauk11 (1956), 199–202.

    Google Scholar 

  • [CG] Clancey, K., Gohberg, I.,Factorization of Matrix Functions and Singular Integral Operators, OT, vol. 3, Birkhäuser-Verlag, Basel, 1981.

    Google Scholar 

  • [FGK] Feldman, I., Gohberg, I., Krupnik, N.,A method of explicit factorization of matrix functions and applications, IEOT18 (1994), 277–302.

    Google Scholar 

  • [GF] Gohberg, I., Feldman, I.,Convolution equations and projection methods for their solutions, Math. Monogr., vol. 41, AMS, Providence, RI, 1974.

    Google Scholar 

  • [GK1] Gohberg, I., Krupnik, N.,Systems of singular integral equations in weighted spaces L p, Soviet Math. Dokl10, (1969), no. 3, 688–691.

    Google Scholar 

  • [GK2] —,On complicated linear singular operators, Amer. Math. Soc. Transl. (2)111 (1978), 121–131.

    Google Scholar 

  • [GK3] —,Banach algebras generated by singular integral operators, Colloquia: Math. Soc. Janos Bolyai5, Hilbert space operators, Tihany (Hungary), 1970, pp. 239–264.

    Google Scholar 

  • [GK4] —,One-Dimensional Linear Singular Integral Equations, Vol. II, General Theory and Applications, OT, vol. 54, Birkhäuser Verlag, Basel, 1992.

    Google Scholar 

  • [HR] Heinig, G., Rost, K.,Algebraic Methods for Toeplitz-like Matrices and Operator, OT, vol. 13, Birkhäuser Verlag, Basel, 1984.

    Google Scholar 

  • [K] Krupnik, N.,Banach Algebras with Symbol and singular Integral Operators, OT, vol. 26, Birkhäuser Verlag, Basel, 1987.

    Google Scholar 

  • [KF] Krupnik, N., Feldman, I.,On the relation between factorization and inversion of finite Toeplitz matrices, Izv. Akad. Nauk Mold. SSR, Fiz.-Tekh. Mat.3 (1985), 20–25, (Russian).

    Google Scholar 

  • [LS] Litvinchuk, G.S. Spitkovsky, I.M.,Factorization of Measurable Matrix Functions, OT, vol. 25, Birkhäuser Verlag, Basel, 1987.

    Google Scholar 

  • [PS] Prösdorf, S., Speck, F.-O.,A factorization procedure for two by two matrix functions on the circle with two rationally independent entries, Proceedings of the Royal Society of Edinburgh115A (1990), 119–138.

    Google Scholar 

  • [S] Simonenko, I.B.,Some general questions in the theory of the Riemann boundary value problem, Math. USSR, Izv.2 (1968), no. 5, 1091–1099.

    Google Scholar 

  • [Sz] Szego, G.,Orthogonal Polynomials, American Mathematical Society Colloquium Publications, vol. 23, 1959.

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Feldman, I., Gohberg, I. & Krupnik, N. On explicit factorization and applications. Integr equ oper theory 21, 430–459 (1995). https://doi.org/10.1007/BF01222017

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