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Hilbert and Hilbert—Samuel polynomials and partial differential equations

✍ Scribed by A. G. Khovanskii; S. P. Chulkov

Publisher
SP MAIK Nauka/Interperiodica
Year
2005
Tongue
English
Weight
155 KB
Volume
77
Category
Article
ISSN
0001-4346

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Using the notion of quantum integers associated with a complex number q = 0, we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q-Jacobi polynomials when |q| < 1, and for the special value q = (1- they are closely related to Hankel

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In 1929, S. Bochner identified the families of polynomials which are eigenfunctions of a second-order linear differential operator. What is the appropriate generalization of this result to bivariate polynomials? One approach, due to Krall and Sheffer in 1967 and pursued by others, is to determine wh