Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics eBook

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.

The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.

Contents:

• Normed Spaces and Banach Spaces
• Hilbert Spaces
• Finite Dimensional Hilbert Spaces
• Hilbert Space L₂(Ω)
• Hilbert Space ℓ₂(II)
• Fourier Transform
• Wavelets
• Holomorphic Entire Functions and Hilbert Space
• Generalized Functions
• Quantum Mechanics

Readership: Advanced undergraduate, graduate and post-graduate students in mathematics and theoretical physics. The book is also suitable for those taking courses in functional analysis and quantum theory.

Key Features:

• Summarizes the different topics in Functional Analysis with applications to Quantum Theory
• Further includes Supplementary Problems and Programming Problems with Solutions