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This volume consists of the proceedings of the NATO Advanced
Research Workshop on Approximation by Solutions of Partial
Differential Equations, Quadrature Formulae, and Related Topics,
which was held at Hanstholm, Denmark. These proceedings include the
main invited talks and contributed papers given during the
workshop. The aim of these lectures was to present a selection of
results of the latest research in the field. In addition to
covering topics in approximation by solutions of partial
differential equations and quadrature formulae, this volume is also
concerned with related areas, such as Gaussian quadratures, the
Pompelu problem, rational approximation to the Fresnel integral,
boundary correspondence of univalent harmonic mappings, the
application of the Hilbert transform in two dimensional
aerodynamics, finely open sets in the limit set of a finitely
generated Kleinian group, scattering theory, harmonic and maximal
measures for rational functions and the solution of the classical
Dirichlet problem. In addition, this volume includes some problems
in potential theory which were presented in the Problem Session at
Hanstholm.
This volume consists of the proceedings of the NATO Advanced
Research Workshop on Approximation by Solutions of Partial
Differential Equations, Quadrature Formulae, and Related Topics,
which was held at Hanstholm, Denmark. These proceedings include the
main invited talks and contributed papers given during the
workshop. The aim of these lectures was to present a selection of
results of the latest research in the field. In addition to
covering topics in approximation by solutions of partial
differential equations and quadrature formulae, this volume is also
concerned with related areas, such as Gaussian quadratures, the
Pompelu problem, rational approximation to the Fresnel integral,
boundary correspondence of univalent harmonic mappings, the
application of the Hilbert transform in two dimensional
aerodynamics, finely open sets in the limit set of a finitely
generated Kleinian group, scattering theory, harmonic and maximal
measures for rational functions and the solution of the classical
Dirichlet problem. In addition, this volume includes some problems
in potential theory which were presented in the Problem Session at
Hanstholm.
This research-level monograph on harmonic maps between singular spaces sets out much new material on the theory, bringing all the research together for the first time in one place. Riemannian polyhedra are a class of such spaces that are especially suitable to serve as the domain of definition for harmonic maps. Their properties are considered in detail, with many examples being given, and potential theory on Riemmanian polyhedra is also considered. The work will serve as a concise source and reference for all researchers working in this field or a similar one.
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