Non-symmetric fast decreasing polynomials and applications

A polynomial Pn is called fast decreasing if Pn(0)=1, and, on [−1,1], Pn decreases fast (in terms of n and the distance from 0) as we move away from the origin. This paper considers the version when Pn has to decrease only on some non-symmetric interval [−a,1] with possibly small a. In this case one gets a faster decrease, and this type of extension is needed in some problems, when symmetric fast decreasing polynomials are not sufficient. We shall apply such non-symmetric fast decreasing polynomials to find local bounds for Christoffel functions and for local zero spacing of orthogonal polynomials with respect to a doubling measure close to a local endpoint.