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＜電子ブック＞
Factorization and Integrable Systems : Summer School in Faro, Portugal, September 2000 / edited by Israel Gohberg, Nenad Manojlovic, Antonio, F. dos Santos
(Operator Theory: Advances and Applications. ISSN:22964878 ; 141)

版	1st ed. 2003.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2003
本文言語	英語
大きさ	VII, 220 p : online resource
著者標目	Gohberg, Israel editor Manojlovic, Nenad editor dos Santos, Antonio, F editor SpringerLink (Online service)
件　名	LCSH:Operator theory LCSH:Differential equations LCSH:Mathematical physics FREE:Operator Theory FREE:Differential Equations FREE:Mathematical Methods in Physics
一般注記	An Overview of Matrix Factorization Theory and Operator Applications -- 0 Introduction -- 1 General theorems -- 2 Factorization in decomposing Banach algebras -- 3 Generalized Lp factorization -- 4 State space method -- References -- Matrix Riemann-Hilbert Problems Related to Branched Coverings of ??1 -- 1 Introduction -- 2 Riemann-Hilbert problem with quasi-permutation monodromies and algebraic curves -- 3 Riemann surfaces. Rauch variational formulas -- 4 Solution of Riemann-Hilbert problems with quasi-permutation monodromies and Szegö kernel -- 5 Isomonodromic tau-function and Cauchy-Riemann determinants -- Acknowledgements -- References -- Quantum Groups and Integrable Models -- 1 Introduction -- 2 Algebraic Bethe Ansatz and QISM -- 3 Yang-Baxter equation -- 4 Thermodynamic limits -- 5 Conclusion -- Acknowledgements -- References -- Integrable Systems and Factorization Problems -- 1 Introduction -- 2 A few preliminaries: Poisson brackets, coadjoint orbits, etc. -- 3 Classical r-matrices and Lax equations -- 4 Classical Yang-Baxter identity -- 5 A finite-dimensional example -- 6 Loop algebras and the Riemann problem -- 7 More examples -- 8 Zero curvature equations -- 9 Difference equations and Poisson-Lie groups -- Acknowledgements -- References -- Programme of the Summer School on Factorization and Integrable Systems In September 2000 a Summer School on "Factorization and Integrable Systems" was held at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field. The lecture notes of the courses have been specially prepared for publication in this volume. The book consists of four contributions. I. Gohberg, M.A. Kaashoek and I.M. Spitkovsky present an extensive review of the factorization theory of matrix functions relative to a curve, with emphasis on the developments of the last 20-25 years. The group-theoretical approach to classical integrable systems is reviewed by M.A. Semenov-Tian-Shansky. P.P. Kulish surveyed the quantum inverse scattering method using the isotropic Heisenberg spin chain as the main example HTTP:URL=https://doi.org/10.1007/978-3-0348-8003-9

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