Functional Analysis: Fundamentals and Applications

The textbook "Functional Analysis" provides a clear and concise introduction to functional analysis, covering distance, integral, norm, Lebesgue spaces, dual spaces, Sobolev spaces, capacity theory, and elliptic problems. The second edition has been improved with expanded coverage of advanced calculus and distribution theory, new proofs, theorems, and applications. It is an excellent resource for students in mathematics and applied mathematics.

Format: Hardback
Length: 251 pages
Publication date: 28 January 2023
Publisher: Birkhauser Verlag AG

This textbook offers a comprehensive and concise introduction to functional analysis, covering fundamental concepts such as distance, integral, and norm, along with their relationships. The first three chapters provide a solid foundation by exploring these notions and presenting fundamental examples, including Lebesgue spaces, dual spaces, and Sobolev spaces.

In the subsequent two chapters, applications to capacity theory and elliptic problems are developed. Notably, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are established using purely functional methods. The epilogue provides a historical overview of functional analysis in relation to integration and differentiation, serving as a valuable resource for students in mathematics and applied mathematics.

The second edition of this textbook further enhances its content by incorporating numerous improvements and additional material. The coverage of advanced calculus and distribution theory has been extensively revised and expanded, offering readers a more comprehensive understanding of these topics. New proofs, theorems, and applications have been added to deepen the reader's understanding and engagement.

Whether you are a student embarking on the study of functional analysis or a professional seeking to advance your knowledge in this field, this textbook is an excellent resource. Its clear and concise writing style, coupled with comprehensive explanations and ample examples, makes it accessible to a wide range of readers. By presenting the principles of functional analysis in a systematic and organized manner, this book helps to establish a strong foundation for further exploration and application in mathematics and related disciplines.

Weight: 571g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031091483
Edition number: 2nd ed. 2022