An Extension of Bochner's Problem: Exceptional Invariant Subspaces - Mathematical PhysicsReport as inadecuate




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Abstract: A classical result due to Bochner characterizes the classical orthogonalpolynomial systems as solutions of a second-order eigenvalue equation. Weextend Bochner-s result by dropping the assumption that the first element ofthe orthogonal polynomial sequence be a constant. This approach gives rise tonew families of complete orthogonal polynomial systems that arise as solutionsof second-order eigenvalue equations with rational coefficients. The resultsare based on a classification of exceptional polynomial subspaces ofcodimension one under projective transformations.



Author: David Gomez-Ullate, Niky Kamran, Robert Milson

Source: https://arxiv.org/







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