普通微分算子的Krall-Laguerre交换代数
Krall-Laguerre commutative algebras of ordinary differential operators
摘要：
1999年，Grunbaum，Haine和Horozov定义了一大类以正交多项式为特征函数的普通微分算子的交换代数.这些多项式是相互正交的Laguerre型权重分布，从而提供解决方案的克拉尔的问题。本文给出了他们的结果的一个新的证明，从而建立了一个关于特征值的对偶交换代数的显式特征的猜想。特别是，对于Koornwinder的推广拉盖尔多项式，我们的方法产生了一个明确的一组发电机的整个代数的微分算子。我们还说明了如何更一般的Sobolev型正交多项式适合在这个理论。
英文摘要：
In 1999, Grunbaum, Haine and Horozov defined a large family of commutative algebras of ordinary differential operators which have orthogonal polynomials as eigenfunctions. These polynomials are mutually orthogonal with respect to a Laguerre-type weight distribution, thus providing solutions to Krall's problem. In the present paper we give a new proof of their result which establishes a conjecture, concerning the explicit characterization of the dual commutative algebra of eigenvalues. In particular, for the Koornwinder's generalization of Laguerre polynomials, our approach yields an explicit set of generators for the whole algebra of differential operators. We also illustrate how more general Sobolev-type orthogonal polynomials fit within this theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
