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Emphasizes the conceptual and historical continuity of analytic function theory. This work covers topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It features chapters on majorization and on functions holomorphic in a half-plane.
Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.
Early in 1952 it became obvious that a new printing would be needed, and new advances in the theory called for extensive revision. It has been completely rewritten, mostly by Phillips, and much has been added while keeping the existing framework. Thus, the algebraic tools play a major role, and are introduced early, leading to a more satisfactory operational calculus and spectral theory. The Laplace-Stieltjes transform methods, used by Hille, have not been replaced but rather supplemented by the new tools. - Foreword.
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Einar Hille is one of the very few mathematicians to make significant contributions to both classical analysis and functional analysis. This volume consists of Hille's own selection of a number of papers that highlight his career in mathematical research. One need only glance through the commentaries at the end of this volume to note that most of Hille's work on functional equations, ordinary differential equations, analytic function theory, ergodic theory, semi-groups, partial differential equations, etc., is germane to presentday research. Thus, this volume should serve as a source of guidance and inspiration for today's budding young analyst.
Biographic Memoirs: Volume 63 contains the biographies of deceased members of the National Academy of Sciences and bibliographies of their published works. Each biographical essay was written by a member of the Academy familiar with the professional career of the deceased. For historical and bibliographical purposes, these volumes are worth returning to time and again.
This book presents a systematic introduction to the theory of holomorphic mappings in normed spaces which has been scattered throughout the literature. It gives the necessary, elementary background for all branches of modern mathematics involving differential calculus in higher dimensional spaces.