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A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a second-order eigenvalue equation. We extend Bochner's result by dropping the assumption that the first element of the orthogonal polynomial sequence be a constant. This approach gives rise to new families of complete orthogonal polynomial systems… (More)

Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunc-tions of Sturm–Liouville problems, but without the assumption that an eigenpolyno-mial of every degree is present. In this sense, they generalize the classical families of Hermite, Laguerre, and Jacobi, and include as a special case the family of CPRS orthogonal polynomials introduced by… (More)

Commons based peer-production (CBPP) is the decentralized , net-based approach to the creation and dissemination of information resources. Underlying every CBPP system is a virtual community brought together by an internet tool (such as a web site) and struc-tured by a specific collaboration protocol. In this talk we will argue that the value of such… (More)

Exceptional orthogonal polynomials were introduced by Gomez-Ullate, Kam-ran and Milson as polynomial eigenfunctions of second order differential equations with the remarkable property that some degrees are missing, i.e., there is not a polynomial for every degree. However, they do constitute a complete orthogonal system with respect to a weight function… (More)

- Peter Crooks, Robert Milson
- 2009

We pose and solve the equivalence problem for subspaces of Pn, the n + 1 dimensional vector space of univariate polynomials of degree ≤ n. The group of interest is PSL 2 acting by projective transformations on the grassmannian variety G k Pn of k-dimensional subspaces. We establish the equivariance of the Wronski map and use this map to reduce the subspace… (More)

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