The Classical Moment is a reexamination of the concept of a supreme moment in the literatures of Greece, Mesopotamia, India, China, Japan, Korea, and Vietnam. Taking the case of Greece as its starting point, it examines what such 'moments' have in common, how they are created, and what effect they have on subsequent literary creation.

This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.

The essays in this book all touch on knowledge and its pleasures. Schall does not tarry on the effort and determination it often takes to say just what we want to say, then say it and know that we have said it. Our writing is our thinking, our thinking-through, our being pleased to know this is it... this is the point Schall, one of America's greatest essayists, makes here.

The mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century. Important connections between the moment problem and many branches of analysis are presented. In this self-contained text, readers will find a unified exposition of important classical results, which are difficult to read in the original journals, as well as a strong foundation for many areas in modern applied mathematics. Researchers in areas that use techniques developed for the classical moment problem will find the book of interest.

The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.

This volume is available on its own or as part of the seven volume set, Greek Literature. This collection reprints in facsimile the most influential scholarship published in this field during the twentieth century. For a complete list of the volume titles in this set, see the listing for Greek Literature [ISBN 0-8153-3681-0]. A full table of contents can be obtained by email: [email protected].