The action of index integral transforms on orthogonal polynomial sequences

Ana Loureiro (University of Kent)

Tuesday 12th November, 2013 16:05-17:00 Maths 417


The discussion will be centred on certain index integral transforms, with a special focus on the Kontorovich-Lebedev transform) mapping d-orthogonal polynomial sequences. These are essentially sequences of polynomials satisfying a recurrence relation of order d+1, which are orthogonal with respect to a vector function of (d-1) weights, where d is an integer greater than or equal to 2. When d equals 2, we recover the standard orthogonality. Among the targeted polynomial sequences are the some semiclassical polynomials whose recurrence coefficients are particular solutions of Painleve equations.

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