|
Factorizability of matrix functions: A direct proof
Author(s):
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
Posted:
November 13, 2008
MathSciNet review:
2411967
Retrieve article in:
PDF
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:
-
- 1.
- B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Internat. Ser. Monogr. Pure Appl. Math., vol. 7, Pergamon Press, New York, 1958. MR 0102719 (21:1505)
- 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, Hamiltonian methods in the theory of solitons, ``Nauka'', Moscow, 1986; English transl., Springer-Verlag, Berlin, 1987. MR 0889051 (89m:58102); MR 0905674 (89m:58103)
- 4.
- S. Novikov, S. V. Manakov, L. E. Pitaevskiĭ, and V. E. Zakharov, Theory of solitons. The inverse scattering method, ``Nauka'', Moscow, 1980; English transl., Consultants Bureau [Plenum], New York, 1984. MR 0573607 (81g:35112); MR 0779467 (86k:35142)
- 5.
- J. Plemelj, Riemannsche Funktionenscharen mit gegebener Monodromiegruppe, Monatsh. Math. Phys. 19 (1908), 211-245. MR 1547764
- 6.
- N. I. Muskhelishvili, Singular integral equations. Boundary problems of function theory and their application to mathematical physics, Gostekhizdat, Moscow-Leningrad, 1946; English transl., Noordhoff Internat. Publ., Leyden, 1977. MR 0020708 (8:586b); MR 0438058 (55:10978)
- 7.
- N. P. Vekua, Systems of singular integral equations and some boundary problems, GITTL, Moscow-Leningrad, 1950; English transl., P. Noordhoff, Ltd., Groningen, 1967. MR 0043346 (13:247a); MR 0211220 (35:2102)
- 8.
- S. G. Michlin and S. Prössdorf, Singuläre Integraloperatoren, Math. Lehrbücher Monogr. II. Abt. Math. Monogr., Bd. 52, Akademie-Verlag, Berlin, 1980. MR 0587117 (82c:45002)
- 9.
- I. Ts. Gokhberg and M. G. Kreĭn, Systems of integral equations on the half-line with kernels depending on the difference of the arguments, Uspekhi Mat. Nauk 13 (1958), no. 2(80), 3-72; English transl., Amer. Math. Soc. Transl. (2), vol. 14, Amer. Math. Soc., Providence , RI, 1960, pp. 217-287. MR 0102720 (21:1506)
- 10.
- F. D. Gakhov, Boundary value problems, Fizmatgiz, Moscow, 1958; English transl., Pergamon Press, Oxford, 1966. MR 0104117 (21:2879); MR 0198152 (33:6311)
- 11.
- S. L. Sobolev, Some applications of functional analysis in mathematical physics, 3rd ed., ``Nauka'', Moscow, 1988; English transl., Transl. Math. Monogr., vol. 90, Amer. Math. Soc., Providence, RI, 1991. MR 0986735 (90m:46059); MR 1125990 (92e:46067)
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
Email:
babich@pdmi.ras.ru
DOI:
10.1090/S1061-0022-08-01035-2
PII:
S 1061-0022(08)01035-2
Received by editor(s):
8/FEB/2007
Posted:
November 13, 2008
Additional Notes:
Supported by RFBR (grant no. 08-01-00511)
Copyright of article:
Copyright
2008,
American Mathematical Society
|
