Lawrence Zalcman – författare

M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, ""The shortest and best way between two truths of the real domain often passes through the imaginary one.'' Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Muntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Zelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime number theorem. Four brief appendices provide all necessary background in complex analysis beyond the standard first year graduate course. Lovers of analysis and beautiful proofs will read and reread this slim volume with pleasure and profit.

M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields. Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.

M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.

M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields. Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences.Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences.Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.