Strong Asymptotic of Cauchy Biorthogonal Polynomials and Orthogonal Polynomials with Varying Measure

We give the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the defining measures are supported on bounded nonintersecting intervals of the real line and satisfy Szegő’s condition. The biorthogonal polynomials are connected with certain mixed type Hermite-Padé polynomials, which verify full orthogonality relations with respect to certain varying measures. Thus, the strong asymptotic of orthogonal polynomials with respect to varying measures plays a key role in the study.