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** ........ published in NEWSLETTER # 47 **

**APPROXIMATION BY SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS**

by Professor M. Goldstein, Arizona State University, Tempe/AZ (U.S.A.)

This volume contains the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations held in Hanstholm, Denmark in July, 1991.

The main topics covered are harmonic, polyharmonic, and complex approximation in the uniform and L exp P norms and applications to such topics as characterisations of balls and strips via harmonic quadrature, and the Ahlfors conjecture that the limit point set of a finitely generated Kleinian group has two dimensional Lebesgue measure zero. Other topics covered are rational approximation, a comparison of harmonic and maximal measures for rational functions, applications of the Hilbert transform in aerodynamics, Gauss quadrature, univalent harmonic mappings, the Pompieu problem, and scattering theory.

This volume (NATO ASI SERIES C365) also contains a list of open research problems which were posed by the participants at the workshop. The papers presented in this volume have already stimulated a large number of research papers which either have appeared since the workshop was held or are in press. In addition, further research on the topics contained in this volume is being pursued by many mathematicians at the present time.

Thus this volume should be very useful to research mathematicians in analysis and applied mathematicians as well.

Reference books: C2, C29, C111, **C365**, C384