In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out.
Discrete Laguerre-Sobolev expansions: A Cohen type inequality
C. Markett在适当的加权$L^{p}$空间中证明了经典Laguerre展开式的一个Cohen型不等式.本文得到了关于离散Laguerre-Sobolev正交多项式的Fourier展开式的一个Cohen型不等式，该多项式具有任意（有限）个质点。因此，我们推广了由于B的结果。Xh. Fejzullahu和F.马塞兰。
On some classical type Sobolev orthogonal polynomials
本文提出了一种构造经典型Sobolev正交多项式的方法。我们考虑两类超几何多项式：${}_2 F_2(-n,1;q,r;x)$和${}_3 F_2(-n,n-1+a+b,1;a,c;x)$（$a,b,c,q,r>0$，$n=0,1,...$），它们分别推广了Laguerre和Jacobi多项式.这些多项式满足以下形式的高阶微分方程：$L y + λ_n D y = 0$，其中$L,D$是多项式系数不依赖于$n$的线性微分算子。对于正整数值的参数$r,c$这些多项式是Sobolev正交多项式与一些明确给出的措施。得到了这些多项式的一些基本性质，包括递推关系。
