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Geometric function theory --- Geometry

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This volume contains the proceedings of a seminar week of invited talks associated with the Workshop "Theoretical and Numerical Aspects of Geometric Variational Problems". The Workshop was conducted between August and October 1990: the seminar week was held from September 24 - 28. The workshop brought together researchers primarily from Australia and Germany working in theoretical and applied mathematics, numerical analysis and computer simulation.

Geometric analysis. --- Geometric function theory.

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In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. The authors then extend the H^infty-functional calculus to an overline{H^infty}+H^infty-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of 2imes 2 partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.

Geometric function theory. --- Operator theory.

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Complex analysis --- Geometric function theory --- Congresses. --- 51 --- -Function theory, Geometric --- Functions of complex variables --- Mathematics --- Congresses --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Function theory, Geometric --- Geometric function theory - Congresses.

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Differential equations --- Geometric function theory --- Chebyshev systems