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Geometric function theory.

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

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This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.

Operator theory. --- Holomorphic functions. --- Geometric function theory. --- Hilbert space.