Abstract
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in terms of the Schur complement of A.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Böttcher, A., Karlovich, YuI: Carleson curves, Muckenhoupt weights, and Toeplitz operators. Birkhäuser Verlag, Basel, Boston (1997)
Conceição, A.C., Kravchenko, V.G., Teixeira, F.S.: Factorization of matrix functions and the resolvents of certain operators, singular integral operators, factorization and applications. Oper. Theory Adv. Appl. 142, 91–100 (2003)
Conceição, A.C., Kravchenko, V.G., Teixeira, F.S.: Factorization of Some Classes of Matrix Functions and the Resolvent of a Hankel Operator, Factorization, Singular Operators and Related Problems (Funchal, 2002), pp. 101–110. Kluwer Acad. Publ, Dordrecht (2003)
Duren, P.L.: Theory of \({H}^p\) Spaces. Academic Press, Cambridge (1970)
Glazman, I.M. Ljubich, J.I.: Finite-dimensional linear analysis. Dover Publications, Inc., Mineola, NY (2006). A systematic presentation in problem form. Translated from the Russian and edited by G. P. Barker and G. Kuerti, Reprint of the 1974 edition (2006)
Gohberg, I., Kaashoek, M.A., Spitkovsky, I.M.: An overview of matrix factorization theory and operator applications, factorization and integrable systems (Faro, 2000). Oper. Theory Adv. Appl. 141, 1–102 (2003). Birkhäuser, Basel
Gohberg, I., Krein, M.G.: Systems of integral equations on a half-line with Kernel depending upon the difference of the arguments. Uspekhi Mat. Nauk 13(2):3–72 (1958) (in Russian). English translation: Am. Math. Soc. Transl.14(2), 217–287 (1960)
Gustafson, K.E., Rao, D.K.M.: Numerical Range. The Field of Values of Linear Operators and Matrices. Springer, New York (1997)
Litvinchuk, G.S., Spitkovskii, I.M.: Factorization of measurable matrix functions, operator theory: advances and applications, vol. 25. Birkhäuser Verlag, Basel (1987). Translated from the Russian by B. Luderer, With a foreword by B. Silbermann. (1987)
Litvinchuk, G.S., Spitkovsky, I.M.: Exact estimates of defect numbers of the generalized Riemann boundary value problem. Dokl. Akad. Nauk SSSR 255(5), 1042–1046 (1980). English translation in Soviet Math. Dokl. 22(3), 781–785 (1980)
Litvinchuk, G.S., Spitkovsky, I.M.: Sharp estimates of the defect numbers of a generalized Riemann boundary value problem, factorization of Hermitian matrix-functions, and some problems on approximation of meromorphic functions. Math. USSR Sb. 45, 205–224 (1983)
Peller, V.V.: Hankel Operators and their Applications. Springer, Berlin (2003)
Spitkovsky, I.M.: The factorization of matrix-valued functions whose Hausdorff set lies inside an angle. Sakharth. SSR Mecn. Akad. Moambe 86(3), 561–564 (1977)
Spitkovsky, I.M.: Some estimates for partial indices of measurable matrix valued functions. Mat. Sb. (N.S.) 111(153)(2), 227–248 (1980), 319 (in Russian). English translation: Math. USSR. Sbornik 39, 207–226 (1981)
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.
Rights and permissions
About this article
Cite this article
Spitkovsky, I.M., Voronin, A.F. A Note on the Factorization of Some Structured Matrix Functions. Integr. Equ. Oper. Theory 90, 39 (2018). https://doi.org/10.1007/s00020-018-2468-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s00020-018-2468-0