New Aspects in Interpolation and Completion Theories

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This volume features eight papers on recent advancements in interpolation theory for matrix functions and completion theory for matrices and operators. The first paper by D. Alpay and P. Loubaton examines a trigonometric moment problem for matrix-valued functions, emphasizing the realization approach in its resolution. The second paper by M. Bakonyi, V. G. Kaftal, G. Weiss, and H. J. Woerdeman addresses a matrix completion problem focusing on the lower triangular part of operator entries. It explores completions with both small usual and Hilbert-Schmidt norms, providing bounds for these norms and highlighting the significance of maximum entropy extensions, with applications to nest algebras and integral operators. The third paper by J. A. Ball, I. Gohberg, and M. A. Kaashoek presents solutions to time-varying interpolation problems, centering on the time-varying analog of the Nevanlinna-Pick tangential problem, where interpolation conditions arise from both sides. The state space theory of time-varying systems is crucial in this context. Together, these papers contribute to the understanding of complex matrix functions and operator theory.