Functional Analysis: Fundamentals and Applications

This textbook presents functional analysis principles in a clear and concise way, covering distance, integral, norm, Lebesgue spaces, dual spaces, Sobolev spaces, capacity theory, and elliptic problems. It includes improvements and supplementary material, such as advanced calculus and distribution theory, new proofs, theorems, and applications.

Format: Paperback / softback
Length: 251 pages
Publication date: 28 January 2024
Publisher: Birkhauser Verlag AG

This textbook offers a comprehensive and accessible introduction to the principles of functional analysis. The first three chapters provide a solid foundation by defining key concepts such as distance, integral, and norm, along with their interconnections. These concepts are then illustrated through fundamental examples, including Lebesgue spaces, dual spaces, and Sobolev spaces. The subsequent chapters delve into applications, particularly in capacity theory and elliptic problems. The isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proven using purely functional methods, showcasing the power of functional analysis. The epilogue provides a historical perspective on the development of functional analysis, connecting it to integration and differentiation. This textbook is an excellent resource for students in mathematics and applied mathematics, offering a clear and concise presentation of the subject matter. The second edition of Functional Analysis includes several enhancements, including a thorough revision of advanced calculus and distribution theory, new proofs, theorems, and applications, and supplementary material for further exploration.

Dimension: 235 x 155 (mm)
ISBN-13: 9783031091513
Edition number: 2nd ed. 2022