Menahem Schiffer

An investigation of finite Riemann surfaces from the point of view of functional analysis, that is, the study of the various Abelian differentials of the surface in their dependence on the surface itself. Many new results are presented. Originally published in 1954. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

An investigation of finite Riemann surfaces from the point of view of functional analysis, that is, the study of the various Abelian differentials of the surface in their dependence on the surface itself. Many new results are presented. Originally published in 1954. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

""Functionals of Finite Riemann Surfaces"" is a comprehensive exploration of the mathematical properties of finite Riemann surfaces, written by Menahem Schiffer. The book is part of the Princeton Mathematical Series, Volume 16, and is intended for advanced students and researchers in the field of mathematics. The book presents a detailed analysis of the functionals that can be defined on finite Riemann surfaces, including the Dirichlet integral, the Bergman kernel, and the Green's function. The author explores the connections between these functionals and the geometry of the surfaces, as well as their relationship to other areas of mathematics such as complex analysis and potential theory. Throughout the book, Schiffer provides numerous examples and applications of the theory, including the study of conformal mappings, harmonic functions, and the Riemann mapping theorem. He also discusses the role of finite Riemann surfaces in the study of algebraic curves and moduli spaces. Overall, ""Functionals of Finite Riemann Surfaces"" is a valuable resource for anyone interested in the mathematical properties of these surfaces and their applications in various areas of mathematics. This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.