Generalized Gonarov Polynomials
نویسندگان
چکیده
We introduce the sequence of generalized Gon£arov polynomials, which is a basis for the solutions to the Gon£arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon£arov basis is a sequence (tn(x))n≥0 of polynomials de ned by the biorthogonality relation εzi(d (tn(x))) = n!δi,n for all i, n ∈ N, where d is a delta operator, Z = (zi)i≥0 a sequence of scalars, and εzi the evaluation at zi. We present algebraic and analytic properties of generalized Gon£arov polynomials and show that such polynomial sequences provide a natural algebraic tool for enumerating combinatorial structures with a linear constraint on their order statistics.
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