Description:

The book offers a clear and thorough introduction to the core principles of functional analysis, bridging the gap between abstract theory and practical applications. It present s rigorous mathematical concepts in a structured and accessible manner, supported by detailed proofs, illustrative examples, and over 300 graded exercises.

Covering essential topics such as metric spaces, normed spaces, Banach and Hilbert spaces, spectral theory, and key theorems including Hahn–Banach, Open Mapping, and Closed Graph, the book aligns closely with Indian university syllabi at both undergraduate and postgraduate levels. Its application-oriented approach extends relevance to related fields such as mathematical physics, differential equations, and quantum mechanics. Whether used as a primary textbook or a supplementary resource, this book equips students, instructors, and researchers with the depth and clarity needed to master this fundamental area of modern mathematics.

KEY FEATURES

• Rigorous yet Accessible Presentation: Clear, step-by-step exposition of abstract concepts, making functional analysis approachable for students at various levels.

• Comprehensive Coverage with Detailed Proofs: In-depth treatment of fundamental theorems, including Hahn–Banach, Open Mapping, and Closed Graph Theorems, building a strong theoretical foundation.

• Extensive Exercise Support: Over 300 graded problems and examples, supplemented by a separate solutions manual on the book's webpage: https://www.phindia.com/Foundations_of_Functional_Analysis_AbhayKumar

• Application-oriented Approach: Includes applications in spectral theory, differential equations, bridging theory and practice.

TARGET AUDIENCE

• M.Sc (Mathematics)

• BE/B.Tech (Engineering Mathematics)