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Einar Hille, Classical Analysis and Functional Analysis
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.
Ordinary Differential Equations in the Complex Domain
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.
Analytic Function Theory
Emphasizes the conceptual and historical continuity of analytic function theory. This book covers canonical topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It also features chapters on majorization and on functions holomorphic in a half-plane.
Analysis
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Functional Analysis and Semi-groups
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.
Analysis
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Biographical Memoirs
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.
Indiscrete Thoughts
Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.
