Elias M. Stein Book order

Focusing on the boundary value theory of holomorphic functions in several complex variables, this book addresses a developing area in mathematical analysis. While the theory is well-established for one variable, its application to multiple variables is more recent and complex, relying on partial differential equations. Professor Stein highlights the potential-theoretic aspects of these boundary value problems, positioning this work as a foundational resource for scholars in the field.

Focusing on the integration of functional analysis, probability theory, and contemporary analysis, this textbook presents these subjects in a student-friendly manner. It features a wealth of engaging exercises and problems, making it an essential resource for learners. The book stands out for its comprehensive approach, bringing together key concepts that have evolved over the past fifty years, thereby enriching the existing literature in the field.

The second volume delves into the fascinating realm of complex analysis, showcasing the elegance of holomorphic functions through foundational theorems like the Cauchy theorems and residues. It explores analytic continuation and the argument principle, while also bridging connections to other mathematical fields. Topics include the Fourier transform via contour integration, the zeta function in relation to the prime number theorem, and an introduction to elliptic functions, highlighting their applications in combinatorics and number theory.