An In-depth Exploration of the Moment Problem: Graduate Texts In Mathematics 277

Moments play a crucial role in various areas of mathematics, statistics, and physics. They offer insights into the characteristics, properties, and behaviors of random variables, probability distributions, and various mathematical objects.

Understanding the Moment Problem

The moment problem is a fundamental concept in mathematical analysis, specifically in the field of functional analysis. It deals with the reconstruction of a function or a probability measure from its moments or a sequence of moments.

The book, "The Moment Problem" published under the Graduate Texts in Mathematics series as book number 277, is a comprehensive guide that delves deep into the theories, techniques, and applications related to the moment problem.

The Moment Problem (Graduate Texts in Mathematics Book 277)

by Konrad Schmüdgen (1st ed. 2017 Edition, Kindle Edition)

5 out of 5

Language	:	English
File size	:	10645 KB
Print length	:	548 pages
Screen Reader	:	Supported

FREE

Overview of "The Moment Problem" Book

"The Moment Problem" by Konrad Schmüdgen is an essential textbook for graduate students, researchers, and scholars interested in mathematics, functional analysis, and probability theory. It provides a thorough exploration of the moment problem and its various aspects.

The book begins with an that lays the foundation for understanding the concept of moments and their importance in mathematical analysis. It then progresses to discuss the classical moment problem, Hamburger moments, and Stieltjes moments.

Throughout the book, Schmüdgen presents theorems, proofs, and examples in a clear and concise manner, ensuring readers can grasp the concepts easily. The book is accompanied by exercises and problems that test the reader's understanding and encourage further exploration.

Applications of the Moment Problem

The moment problem finds applications in various fields, including but not limited to:

1. Probability Theory

   In probability theory, the moment problem plays a crucial role in determining the characteristics of random variables and probability distributions. Moments can provide insights into the mean, variance, skewness, and kurtosis of a distribution.

2. Signal Processing

   In signal processing, moments are utilized for various purposes such as filtering, noise reduction, and feature extraction. They help in characterizing signals and determining their similarities or differences.

3. Image Analysis

   In image analysis, moments are used to describe the shape, orientation, and other features of objects in an image. This enables automated image recognition, segmentation, and understanding.

The Significance of "The Moment Problem" Book

"The Moment Problem" stands out as an invaluable resource for researchers and students due to its comprehensive coverage of the moment problem. The book provides a solid theoretical foundation coupled with practical applications, ensuring readers can grasp the concepts and apply them to real-world scenarios.

By studying and understanding "The Moment Problem," readers can gain a deeper insight into the mathematical intricacies and complexities involved in moment analysis. They can explore the rich history, theorems, and techniques developed within this field of mathematics.

The moment problem is a fascinating mathematical concept that has far-reaching implications in various scientific disciplines. "The Moment Problem" book, part of the Graduate Texts in Mathematics series, offers a comprehensive guide to understanding and applying the theories and techniques related to moments.

Whether you are a graduate student, researcher, or simply an enthusiast in mathematics, acquiring "The Moment Problem" book will undoubtedly enhance your knowledge and deepen your appreciation of this fundamental mathematical concept.

The Moment Problem (Graduate Texts in Mathematics Book 277)

by Konrad Schmüdgen (1st ed. 2017 Edition, Kindle Edition)

5 out of 5

Language	:	English
File size	:	10645 KB
Print length	:	548 pages
Screen Reader	:	Supported

FREE

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.