Author: Wiley
Introductory Functional Analysis with Applications by Erwin Kreyszig, published by Wiley, is a widely respected graduate-level textbook that introduces the fundamental concepts of functional analysis in a clear and accessible manner. It covers essential topics such as normed spaces, Banach spaces, inner product spaces, and Hilbert spaces, laying a strong foundation for further study. The book also delves into important theorems like the Hahn-Banach Theorem, the Open Mapping Theorem, and the Uniform Boundedness Principle. A significant portion is dedicated to the study of bounded linear operators and their applications, making the book particularly useful for students of applied mathematics, physics, and engineering. Spectral theory, compact operators, and self-adjoint operators are also discussed, particularly in the context of Hilbert spaces. Unlike more abstract treatments, Kreyszig’s approach emphasizes practical applications, including examples from differential and integral equations. One of the strengths of this text is its minimal reliance on advanced prerequisites—basic knowledge of linear algebra and real analysis is sufficient. The book is known for its clarity and rigorous explanations, making it a popular choice for first-time learners of functional analysis. First published in 1978, it remains a staple in many university curricula and has been reprinted in various editions, including the Wiley Classics Library. With approximately 688 pages, the text remains one of the most accessible and application-focused introductions to the subject.