Multivariable complex analysis and harmonic analysis provide efficient techniques to study many applied mathematical problems. The main objective of a conference held in Bordeaux in June 1995, in honour of Professor Roger Gay, was to connect these mathematical fields with some of their applications. This was also the guideline for the fourteen contributions collected in this volume.

Besides presenting new results, each speaker made a substantial effort in order to present an up to date survey of his field of research. All the subjects presented here are very active domains of research: integral geometry (with its relation to X-ray tomography), classical harmonic analysis and orthogonal polynomials, pluricomplex potential theory (with its deep connection with polynomial approximation), complex analytic methods in the theory of partial differentiable operators with constant coefficients (in the spirit of those initiated by Leon Ehrenpreis), Calderon-Zygmund operators and nonlinear operators, oscillatory integrals and resonance, and finally multivariable residue theory in its most recent developments. It is hoped that the reader will find enough insight in the different survey papers presented here to become involved with one of these subjects or to pursue further applications.

Preface
The Pompieu problem, what is new?
Injectivity of the spherical mean operator and related problems
Applications de la transformation G a une interpolation de fonctions harmoniques de type exponentiel
Operateurs differentiels dEuler-Poisson Darboux generalises et fonctions hypergeometriques de plusieurs variables
Analytic functionals and harmonic functionals
Extremal plurisubharmonic functions for conves bodies in n
Pluricomplex Green functions and approximation of holomorphic functions
Bernstein regions for elliptic operators in two dimensions
[Greek l.c. omega]-hyperbolicity of linear partial differential operators with
constant coefficients
Quelques resultats recents en optique geometrique non lineaire
Progres recents sur le probleme de la racine carree de Kato
Boundary values of regular functions of quaternionic variables
Interpretation of the composed residue homomorphisms by the residual currents
Defining the residue of a complete intersection

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