Published January 18, 2025 | Version v1
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Explicit Factorization of Piecewise Constant Matrix Functions

Authors/Creators

  • 1. Faculty of Exact and Natural Sciences, Tbilisi State University, 2 Chavchadze ave., Tbilisi, 0179, Georgia
  • 2. Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi, 129188, UAE

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https://cagroup.ge/media/research/draaft_SP_Gio.pdf

Funding

European Commission
EffectFact - Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications 101008140

References

  • [1] Adukov V. M. Wiener-Hopf factorization of piecewise meromorphic matrixvalued functions. Sb. Math. 2009; 200:8, 1105-1126. [2] Adukov V. M. Algorithm of polynomial factorization and its implementation in Maple. Vestnik SUSU. 2018; 11:4, 110-122. 3] Anosov D., A. Bolibruch. The Riemann-Hilbert Problem. Vieweg+Teubner Verlag, 1994 [4] Bolibrukh A. A. On sufficient conditions for the existence of a Fuchsian equation with prescribed monodromy. J. Dynam. Control Systems. 1995; 1:2, 329-352. [5] Gakhov F. Riemann's boundary problem for a system of n pairs of functions, Uspekhi Mat. Nauk, 7:4(50) (1952), 3-54. [6] Ehrhardt T., Spitkovsky I. M. Factorization of piecewise constant matrix functions and systems of linear differential equations. St. Petersburg Math. J. 2002; 13:6, 939-991. [7] Giorgadze G., Gulagashvili G. On the splitting type of holomorphic vector bundles induced from regular systems of differential equation. Georgian Mathematical Journal. Vol. 29, N 1, 2022, 25-35. [8] Giorgadze, G., Gulagashvili G. Riemann-Hilbert Boundary Value Problem with Piecewise Constant Transition Function. J. Dyn. Control Syst. 28, 109-119 (2022). https://doi.org/10.1007/s10883-020-09524-z [9] Gohberg G., Kaashoek M.A., Spitkovsky 1.M. An Overview of Matrix Factorization Theory and Operator Applications.Operator Theory: Advances and Applications, Vol. 141, 1-102, 2003 [10] Conddington E., Lewinson N. The Theory of Ordinary Differential Equations. McGram-Hill Book Company, Inc., 1955 [11] Ilyashenko Yu., Yakovenko S. Lectures on Analytic Differential Equations. Am. Math. Soc., Providence, RI, 2007. [12] Katz N. Rigid lokal system. Annals of Mathematics Studies, vol.139, 1996 [13] Kimura T., Shima K. A note on the monodromy of the hypergeometric differential equation. Japan. J. Math. vol.17, N 1. 1991 [14] Khovanskii A. Topological Galois Theory. Solvability and Non-Solvability of Equations in Finite Terms. Springer, 2009 [15] Litvinchuk G, Spitkovski I. Factorization of measurable matrix functions. Birkh¨auser Verlag, (1987) [16] Muskhelishvili N.I. Singular Integral Equations. Noordhoff, Groningen, 1963. [17] Ryabov A. A. Splitting types of vector bundles constructed from the monodromy of a given Fuchsian system. Comput. Math. and Math. Phys. 2004; 44:4, 640-648. [18] Spitkovsky I. Factorization of measurable matrix-functions in classes Lp;P with power weight. Soviet Math. (Iz. VUZ) 32 (1988), no. 5, 78-88. [19] Van der Put M.,Singer M. Galois Theory of Linear Differential Equations. Springer Science & Business Media, 2003 [20] Vyugin I.V., Gontsov R.R., On the question of solubility of Fuchsian systems by quadratures, Russian Math. Surveys 67 (2012), 585-587.