Book:Amol Sasane/A Friendly Approach to Functional Analysis
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Amol Sasane: A Friendly Approach to Functional Analysis
Published $\text {2017}$, World Scientific Publishing
- ISBN 978-1786343338
Subject Matter
Contents
- Preface
- 1.1 Vector spaces
- 1.2 Normed spaces
- 1.5 Compact sets
- 2. Continuous and linear maps
- 2.1 Linear transformations
- 2.2 Continuous maps
- 2.3 The normed space $\map {CL} {X,Y}$
- 2.4 Composition of continuous linear transformations
- 2.5 (*) Open Mapping Theorem
- 2.6 Spectral Theory
- 2.7 (*) Dual space and the Hahn-Banach Theorem
- 3. Differentiation
- 3.1 Definition of the derivative
- 3.2 Fundamental theorems of optimisation
- 3.3 Euler-Lagrange equation
- 3.4 An excursion in Classical Mechanics
- 4. Geometry of inner product spaces
- 4.1 Inner product spaces
- 4.2 Orthogonality
- 4.3 Best approximation
- 4.4 Generalised Fourie series
- 4.5 Riesz Representation Theorem
- 4.6 Adjoints of bounded operators
- 4.7 An excursion in Quantum Mechanics
- 5. Compact operators
- 5.1 Compact operators
- 5.2 The set $\map K {X,Y}$ of all compact operators
- 5.3 Approximation of compact operators
- 5.4 (*) Spectral Theorem of Compact Operators
- 6. A glimpse of distribution theory
- 6.3 Weak solutions
- Solutions
- The Lebesgue integral
- Bibliography
- Index