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The Madison Symposium on Complex Analysis
Edited by: Edgar Lee Stout and Alexander Nagel
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Contemporary Mathematics
1992; 478 pp; softcover
Volume: 137
ISBN-10: 0-8218-5147-0
ISBN-13: 978-0-8218-5147-0
List Price: US$60 Member Price: US$48
Order Code: CONM/137

This volume contains the proceedings of a Symposium on Complex Analysis, held at the University of Wisconsin at Madison in June 1991 on the occasion of the retirement of Walter Rudin. During the week of the conference, a group of about 200 mathematicians from many nations gathered to discuss recent developments in complex analysis and to celebrate Rudin's long and productive career. Among the main subjects covered are applications of complex analysis to operator theory, polynomial convexity, holomorphic mappings, boundary behavior of holomorphic functions, function theory on the unit disk and ball, and some aspects of the theory of partial differential equations related to complex analysis. Containing papers by some of the world's leading experts in these subjects, this book reports on current directions in complex analysis and presents an excellent mixture of the analytic and geometric aspects of the theory.

Reviews

"Among the authors are some of the world's leading experts. Therefore this volume is an excellent report on current directions in complex analysis. It is a tribute to Walter Rudin in so far as much of the work contained in this book makes contact with work that he has done over the last forty years."

-- Monatshefte für Mathematik

• P. Ahern and W. Rudin -- Hulls of $$3$$-spheres in $$\mathbb C^3$$
• H. Alexander -- On the totally real spheres of Ahern and Rudin and Weinstein
• E. Amar -- Dominant sets on the unit sphere of $$\mathbb C^n$$
• S. Bell -- The Cauchy transform, the Szegö projection, the Dirichlet problem, and the Ahlfors map
• C. Berenstein, D.-C. Chang, D. Pascuas, and L. Zalcman -- Variations on the theorem of Morera
• F. Berteloot -- A remark on local continuous extension of proper holomorphic mappings
• T. Bloom -- A multivariable version of the Müntz-Szasz theorem
• J. Bruna and J. M. Ortega -- On $$A^\infty$$ interpolating sets lying on curves
• L. Bungart -- Vanishing cup products on pseudoconvex $$CR$$ manifolds
• J. F. Carlson and D. N. Clark -- Ext for Hilbert modules
• D.-C. Chang, S. G. Krantz, and E. M. Stein -- Hardy spaces and elliptic boundary value problems
• J. Chaumat and A.-M. Chollet -- Représentation intégral de certaines classes de jets de Whitney
• M. Christ -- A class of hypoelliptic PDE admitting non-analytic solutions
• W. C. Connett and A. L. Schwartz -- Fourier analysis off groups
• B. Coupet -- Uniform extendibility of automorphisms
• D. Cruz-Uribe SFO -- The class L log L with weights
• J. P. D'Angelo -- The geometry of proper holomorphic maps between balls
• P. Duren, D. Khavinson, H. S. Shapiro, and C. Sundberg -- Contractive zero-divisors in Bergman spaces
• F. Forelli -- The theorem of F. and M. Riesz for unbounded measures
• F. Forstnerič -- Intersections of analytic and smooth discs
• J. E. Fornæss and N. Sibony -- Critically finite rational maps on $$\mathbb P^2$$
• J. Globevnik -- A disc in the ball approaching the boundary non-nontangentially
• A. A. Himonas -- On hypoellipticity for sums of squares of vector fields
• F. Jafari -- Composition operators in Bergman spaces on bounded symmetric domains
• S. Kaliman -- Isotopic embeddings of affine algebraic varieties into $$\mathbf C^n$$
• W. Królikowski and E. Ramírez de Arellano -- Polynomial solutions of the Fueter-Hurwitz equation
• S.-Y. Li -- Corona problem of several complex variables
• D. Ma -- Sharp estimates of the Kobayashi metric near strongly pseudoconvex points
• P. R. Mercer -- Proper maps, complex geodesics and iterates of holomorphic maps of convex domains in $${\mathbf C}^n$$
• C. Mueller -- On the polynomial hull of two balls
• Y. Nishimura -- Analytic automorphisms of $$\mathbf C^2$$ which preserve the coordinate axes
• M. Putinar and N. Salinas -- Analytic transversality and Nullstellensatz in Bergman space
• J. P. Rosay -- On the radial maximal function and the Hardy Littlewood maximal function in wedges
• M.-C. Shaw -- Local and semi-global existence theorems for $$\overline \partial _b$$ on $$CR$$ manifolds
• D. Sarason -- Making an outer function from two inner functions
• A. Stanoyevitch -- Arclength formulas in conformal mapping
• D. A. Stegenga and K. Stephenson -- Sharp geometric estimates of the distance to VMOA
• E. L. Stout -- On the one-dimensional extension property
• T. V. Tonev -- Analytic $$\Gamma$$-almost-periodic structures in algebra spectra
• D. C. Ullrich -- Recurrence for lacunary cosine series
• J. Wermer -- Maximum modulus algebras