Some Inverse Problems for d-Orthogonal Polynomials

This paper is devoted to the study of the generalized inverse problem of the left product of a d-dimensional vector form by a polynomial. The objective is to find the regularity conditions of the vector linear form defined by , where is a d x d matrix polynomial. In such a case, the d-OPS {Q (n) } (n a parts per thousand yen 0) corresponding to is d-quasi- orthogonal of order l with respect to . Secondly, we study the inverse problem: Given a d -OPS P (n) (n a parts per thousand yen 0) with respect to , characterize the parameters such that the sequence Q(n+dl) = Pn+dl + Sigma(dl)(i=1) a(n+dl)((i)) Pn+dl-i, n >= 0, is d-orthogonal with respect to some regular vector linear form . As an immediate consequence, find the explicit relation between and U and V.