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A version of Fundamental Theorem of Algebra We consider the wide class of Nikishin systems of functions. Such systems are made up of Cauchy transforms of measures (with a special structure) supported on the same interval. We show that generalized polynomials made up of polynomial combinations of the functions in the Nikishin system verify a version of the fundamental theorem of algebra. This result has multiple applications in the asymptotic theory of multiple orthogonal polynomials and in the convergence theory of Hermite-Padé approximation. In particular, we give very general conditions under which the sequence of type II Hermite-Padé approximations of a Nikishin system of functions converges uniformly on each compact subset of the complement of the interval supporting the measures.
Qualquer informação acerca dos seminários pode ser obtida por
correio electrónico para seminarios@mat.ubi.pt.
Departamento de Matemática da Universidade da Beira Interior |