Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Factorizability of matrix functions: A direct proof

Author: V. M. Babich
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 20 (2008), nomer 1.
Journal: St. Petersburg Math. J. 20 (2009), 1-22
MSC (2000): Primary 30E25
Published electronically: November 13, 2008
MathSciNet review: 2411967
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The factorization theorem mentioned in the title is about matrix-valued functions satisfying the Lipschitz condition on the real line and is related to the Riemann problem.

References [Enhancements On Off] (What's this?)

  • 1. B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, International Series of Monographs on Pure and Applied Mathematics. Vol. 7, Pergamon Press, New York-London-Paris-Los Angeles, 1958. MR 0102719
  • 2. R. Mittra and S. W. Lee, Analytical techniques in the theory of guided waves, Macmillan, New York, 1971.
  • 3. L. A. Takhtadzhyan and L. D. Faddeev, \cyr Gamil′tonov podkhod v teorii solitonov, “Nauka”, Moscow, 1986 (Russian). MR 889051
    L. D. Faddeev and L. A. Takhtajan, Hamiltonian methods in the theory of solitons, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987. Translated from the Russian by A. G. Reyman [A. G. Reĭman]. MR 905674
  • 4. V. E. Zaharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskiĭ, \cyr Teoriya solitonov, “Nauka”, Moscow, 1980 (Russian). \cyr Metod obratnoĭ zadachi. [The method of the inverse problem]. MR 573607
    S. Novikov, S. V. Manakov, L. P. Pitaevskiĭ, and V. E. Zakharov, Theory of solitons, Contemporary Soviet Mathematics, Consultants Bureau [Plenum], New York, 1984. The inverse scattering method; Translated from the Russian. MR 779467
  • 5. J. Plemelj, Riemannsche Funktionenscharen mit gegebener Monodromiegruppe, Monatsh. Math. Phys. 19 (1908), no. 1, 211–245 (German). MR 1547764,
  • 6. N. I. Mushelišvili, Singulyarnye Integral′nye Uravneniya. Graničnye Zadači Teorii Funkciĭ i Nekotorye ih Priloženiya k Matematičeskoĭ Fizike, OGIZ, Moscow-Leningrad,], 1946 (Russian). MR 0020708
    N. I. Muskhelishvili, Singular integral equations, Noordhoff International Publishing, Leyden, 1977. Boundary problems of function theory and their application to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted of the 1958 edition. MR 0438058
  • 7. N. P. Vekua, Sistemy singulyarnyh integral′nyh uravneniĭ i nekotorye graničnye zadači, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad,], 1950 (Russian). MR 0043346
    N. P. Vekua, Systems of singular integral equations, P. Noordhoff, Ltd., Groningen, 1967. Translated from the Russian by A. G. Gibbs and G. M. Simmons. Edited by J. H. Ferziger. MR 0211220
  • 8. S. G. Michlin and S. Prössdorf, Singuläre Integraloperatoren, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], vol. 52, Akademie-Verlag, Berlin, 1980 (German). MR 587117
  • 9. I. C. Gohberg and M. G. Kreĭn, Systems of integral equations on the half-line with kernels depending on the difference of the arguments, Uspehi Mat. Nauk (N.S.) 13 (1958), no. 2 (80), 3–72 (Russian). MR 0102720
  • 10. F. D. Gahov, \cyr Kraevye zadachi, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958 (Russian). MR 0104117
    F. D. Gakhov, Boundary value problems, Translation edited by I. N. Sneddon, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. MR 0198152
  • 11. S. L. Sobolev, \cyr Nekotorye primeneniya funktsional′nogo analiza v matematicheskoĭ fizike, 3rd ed., “Nauka”, Moscow, 1988 (Russian). MR 986735
    S. L. Sobolev, Some applications of functional analysis in mathematical physics, Translations of Mathematical Monographs, vol. 90, American Mathematical Society, Providence, RI, 1991. Translated from the third Russian edition by Harold H. McFaden; With comments by V. P. Palamodov. MR 1125990

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 30E25

Retrieve articles in all journals with MSC (2000): 30E25

Additional Information

V. M. Babich
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Received by editor(s): February 8, 2007
Published electronically: November 13, 2008
Additional Notes: Supported by RFBR (grant no. 08-01-00511)
Article copyright: © Copyright 2008 American Mathematical Society