 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
|
|
The Moment Problem
出版済み 3週間でお届けいたします。
1st ed. 2017 Series: Graduate Texts in Mathematics Author: Schmudgen, Konrad Publisher: Springer ISBN: 9783319645452 Cover: HARDCOVER Date: 2017年11月 DESCRIPTION 最新の本書では、包括的かつ統合的にまとめたモーメント問題を提供する。 現代法と最新の進展を含む、古典的な一次元理論と多次元の一般論を網羅。一次元理論と多次元の一般論のいずれにおいても、fullモーメント問題とtruncatedモーメント問題をそれぞれ丁寧に論じている。基本的概念、結果や方法を詳細に展開し、多くの事例と演習問題を設ける。実代数幾何学やヒルベルト空間作用素といった、強力な現代技術に特に焦点を当てる。indeterminateモーメント問題についてはNevanlinnaパラメタリゼーション、truncatedモーメント問題については正準かつ主要な方法、Positivstellensatzeとsemi-algebraic setのモーメント問題間の相互作用、ファイバー定理、多次元決定性理論（multidimensional determinacy theory）、作用素論的アプローチ、存在理論や重要な多次元のtruncatedモーメント問題の特集等、重要な側面を幅広く網羅する。 モーメント問題、関数解析、複素解析、調和解析、実代数幾何学、多項式最適化やシステム理論に取り組む大学院生や研究者に本書は特に役立つだろう。背景情報や理論を図解した様々な課題の演習問題を収載した本書は、モーメント問題の参考書として、また自己学習にも役立つ一冊である。 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 Positivstellensatze 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. TABLE OF CONTENTS Preface and Overview.- 1 Integral representations of linear functionals.- 2 Moment problems on abelian *-semigroups.- Part I The one dimensional moment problem.- 3 One dimensional moment problems on intervals: existence.- 4 One dimensional moment problems: determinacy.- 5 Orthogonal polynomials and Jacobi operators.- 6 The operator-theoretic approach to the Hamburger moment problem.- 7 The indeterminate Hamburger moment problem.- 8 The operator-theoretic approach to the Stieltjes moment problem.- Part II The one dimensional truncated moment problem.- 9 The one-dimensional truncated Hamburger and Stieltjes moment problems.- 10 The one-dimensional truncated moment problem on a bounded interval.- 11 The moment problem on the unit circle.- Part III The multidimensional moment problem.- 12 The moment problem on compact semi-algebraic sets.- 13 The moment problem on closed semi-algebraic sets: existence.- 14 The multidimensional moment problem: determinacy.- 15 The complex moment problem.- 16 Semidefinite programming and polynomial optimization.- Part IV The multidimensional truncated moment problem.- 17 Multidimensional truncated moment problems: existence criteria.- 18 Multidimensional truncated moment problems: basic concepts and special topics.- 19 The truncated moment problem for homogeneous polynomials.
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
