Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials |
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| Authors: | V P Spiridonov S Tsujimoto A S Zhedanov |
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| Institution: | (1) Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow Region, 141980, Russia;(2) Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;(3) Donetsk Institute for Physics and Technology, Donetsk, 83114, Ukraine |
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| Abstract: | The notion of Frobenius-Stickelberger-Thiele (FST) polynomials is introduced. Spectral transformations for these polynomials
analogous to the Christoffel and Geronimus transformations for orthogonal polynomials are constructed. They yield an integrable
discrete time chain (the FST chain) related to the generalized  -algorithm. Relations of the FST polynomials to the Padé interpolation problem and to general and symmetric biorthogonal
rational functions are considered in detail.
This work is supported in part by the Russian Foundation for Basic Research (RFBR) grant no. 06-01-00191 and the Grant-in-Aid
for Scientific Research no. 15540119 from the Ministry of Education, Culture, Sports, Science and Technology, Japan. |
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