Introductory Functional Analysis with Applications - Kreyszig, Erwin (New Delhi: Wiley, 2006)
Functional analysis is a form of mathematical analysis that originated from classical analysis. It is finding increasing applications in mathematics and in natural sciences. This book, Introductory Functional Analysis With Applications, is intended to introduce and explain the subject to college students. So, it focuses on the fundamental principles, theory and also their practical applications. The book covers, among other things, Banach Spaces, Metric Spaces and Hilbert Spaces. It explains the Spectral Theory of Linear Operators in Normed Spaces and the Fundamental Theorems for Normed and Banach Spaces. It also goes into Unbounded Linear Operators in Hilbert Spaces. In each section, the author first outlines the theory he is going to cover, then shows why the concept is essential. The problems given in the book help the students further understand the principles explained in the book. These exercises provide the student with practice at applying the concepts learnt to solve problems. The book also provides illustrations of practical applications of the theorems covered. It touches on the practical uses of these principles, not just in mathematics, but also in other branches of study like physics. Introductory Functional Analysis With Applications helps the students understand the importance of the subject of functional analysis and its use in various fields. It uses the concepts covered in the book to help the students understand the basics of quantum theory. This book provides a clear and practical introduction to the principles and applications of functional analysis.
Appendix 609-680p.; Index 681-688p.
Keywords: Banach spaces; Linear operators; Spectral theory; Metric spaces