関西可積分系セミナー (2004年10月19日)
- 日時
- 2004年10月19日（火）16時30分-17時45分
- 場所
- 京都大学本部キャンパス工学部総合校舎４０６セミナー室
Alexei Zhedanov (Donetsk Inst. Phys. Tech.)
Regular algebras of dimension 2, rational interpolation and biorthogoanl rational functions
We show that the problem of self-similarity in Darboux transformation for generalized eigenvalue problem leads naturally to regular algebras of dimension 2. One of such algebras is the Weyl commutation relation AB=qBA. In turn, realization of these algebras in terms of tri-diagonal operators lead to biorthogonal rational functions. In special cases we obtain explicit rational interpolation of the exponential and power function.