On rank variation of block matrices generated by Nevanlinna matrix functions

Abstract

Key words Nevanlinna matrix function, Hermitian measure on the real axis, block moment matrix, generalized block Pick matrix, generalized block Loewner matrix MSC (2000) 47A57, 30E05, 47A56Within the framework of the multiple Nevanlinna-Pick matrix interpolation and its related matrix moment problem, we study the rank of block moment matrices of various kinds, generalized block Pick matrices and generalized block Loewner matrices, as well as their Potapov modifications, generated by Nevanlinna matrix functions, and derive statements either on rank (or inertia) invariance in different senses or on rank variation of such types of block matrices.