Haine, Luc
[UCL]
Iliev, P
Krall's polynomials are orthogonal polynomials that are also eigenfunctions of a differential operator. We exhibit an analogue of Krall's polynomials within the context of rank-one commutative rings of difference operators. The corresponding spectral curves are unicursal curves with equations v(2) = u(2R+1) (u + 1)(2S+1), R = 0, 1, 2,..., S = 0, 1, 2,.... Our analogues of Krall's polynomials are rational functions, which satisfy an orthogonality relation on the circle. The proof of the orthogonality relations combines the discrete Kadomtsev-Petviashvili bilinear identities, the cuspidal character of the singularities of the spectral curves, together with an extra symmetry of the problem.
Bibliographic reference |
Haine, Luc ; Iliev, P. A rational analogue of the Krall polynomials.Kowalevski Workshop on Mathematical Methods of Regular Dynamics (UNIV LEEDS, LEEDS
(England), Apr 12-15, 2000). In: Journal of Physics A: Mathematical and General, Vol. 34, no. 11, p. 2445-2457 (2001) |
Permanent URL |
http://hdl.handle.net/2078.1/61989 |