Principles of Analysis: Measure, Integration, Functional Analysis, and Applications

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications is a comprehensive textbook that covers the fundamentals of measure, integration, functional analysis, and their applications. It is designed for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level, as well as for qualifying exams in real analysis. The book is divided into four sections, each covering different topics, and includes direct and concise proofs, a variety of examples, and nearly 700 exercises. The author, Hugo D. Junghenn, is a professor of mathematics at The George Washington University and has published numerous journal articles and books in the field.

Format: Paperback / softback
Length: 540 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications is a comprehensive textbook designed to prepare readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. It also serves as a valuable resource for preparing for qualifying exams in real analysis. The book is meticulously crafted to cater to the needs of both readers and instructors, allowing them to select topics that align with their specific interests and requirements.

The author presents the text in a clear and straightforward manner, making it accessible to a wide range of students. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration, and functional analysis.

The book encompasses a wide range of detailed topics, making it a valuable reference for both scholars and practitioners in the field. It is organized into four distinct sections:

Part I: Develops the general theory of Lebesgue integration, providing a solid foundation for subsequent chapters.

Part II: Presents a course in functional analysis, covering various topics such as measure-theoretic functional analysis, operator theory, and Banach spaces.

Part III: Discusses advanced topics in functional analysis, building on the material covered in the previous parts.

Part IV: Includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem, which are essential tools in real analysis.

Additionally, a preliminary chapter covers the theory of metric spaces and general topological spaces, providing a solid foundation for the subsequent chapters.

Features:

Contains direct and concise proofs with attention to detail, making the text easy to understand and follow.

Offers a substantial variety of interesting and nontrivial examples, helping readers to apply the theoretical concepts in real-world scenarios.

Includes nearly 700 exercises ranging from routine to challenging, with hints for the more difficult exercises.

Provides an eclectic set of special topics and applications, expanding the scope of the textbook beyond traditional functional analysis.

About the Author:

Hugo D. Junghenn is a professor of mathematics at The George Washington University. He has published numerous journal articles in the field of analysis and has extensive experience in teaching advanced mathematics courses. His research interests include measure theory, functional analysis, and operator theory.

Weight: 988g
Dimension: 253 x 177 x 33 (mm)
ISBN-13: 9781032476216