Resumen de Measurable diagonalization of positive definite matrices

Yamilet Quintana, José Manuel Rodríguez García

• In this paper we show that any positive definite matrix V with measurable entries can be written as V=UɅU* , where the matrix is diagonal, the matrix U is unitary, and the entries of U and Ʌ are measurable functions (U* denotes the transpose conjugate of U).

  This result allows to obtain results about the zero location and asymptotic behavior of extremal polynomials with respect to a generalized non-diagonal Sobolev norm in which products of derivatives of different order appear. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials.