The origins of Schur research lie in a 1917 article through Issai Schur during which he built a numerical series to correspond to a holomorphic contractive functionality at the unit disk. those sequences at the moment are often called Schur parameter sequences. Schur research has grown considerably considering its beginnings within the early 20th century and now includes a large choice of difficulties regarding numerous periods of holomorphic features and their matricial generalizations. those difficulties comprise interpolation and second difficulties in addition to Schur parametrization of specific periods of contractive or nonnegative Hermitian block matrices.
This booklet is essentially dedicated to issues relating to matrix types of classical interpolation and second difficulties. the foremost subject matters comprise Schur research of nonnegative Hermitian block Hankel matrices and the development of Schur-type algorithms. This ebook additionally covers a few fresh advancements in orthogonal rational matrix services, matrix-valued Carathéodory features and maximal weight strategies for specific matricial second difficulties at the unit circle.
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