Tangential Nevanlinna-Pick Interpolation and Its Connection with Hamburger Matrix Moment Problem

This paper is concerned with the solution of a certain tangentialNevanlinna-Pick interpolation for Nevanlinna functions. We use the so-calledblock Hankel vector method to establish two intrinsic connections betweenthe tangential Nevanlinna-Pick interpolation in the Nevanlinna class and thetruncated Hamburger matrix moment problem associated with the block Hankelvector under consideration: one is a congruent relationship between theirinformation matrices, and the other is a divisor-remainder connection betweentheir solutions. These investigations generalize our previous work onthe Nevanlinna-Pick interpolation and power matrix moment problem.