Abstract
A stronger notion of nonnegative linearization of orthogonal polynomials is introduced. It requires that also the associated polynomials of any order have nonnegative linearization property. This turns out to be equivalent to a maximal principle of a discrete boundary value problem associated with orthogonal polynomials through the three term recurrence relation. The property is stable for certain perturbations of the recurrence relation. Criteria for the strong nonnegative linearization are derived. The range of parameters for the Jacobi polynomials satisfying this new property is determined.
This work was partially supported by KBN (Poland) under grant 5 P03A 034 20 and by European Commission via TMR network “Harmonic Analysis and Related Problems,” RTN2-2001-00315.
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Szwarc, R. (2005). Strong Nonnegative Linearization of Orthogonal Polynomials. In: Ismail, M.E., Koelink, E. (eds) Theory and Applications of Special Functions. Developments in Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/0-387-24233-3_21
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DOI: https://doi.org/10.1007/0-387-24233-3_21
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