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### Functional Analysis and its Applications by Amol Sasane

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Functional Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books. Functional Analysis and its Applications written by Amol Sasane . This is an other book of mathematics cover the following topics.

• 1. Normed and Banach spaces
1.1 Vector spaces
1.2 Normed spaces
1.3 Banach spaces
1.4 Appendix: proof of H¨older’s inequality

• 2. Continuous maps
2.1 Linear transformations
2.2 Continuous maps
2.2.1 Continuity of functions from R to R
2.2.2 Continuity of functions between normed spaces
2.3 The normed space L (X, Y )
2.4 The Banach algebra L (X). The Neumann series
2.5 The exponential of an operator
2.6 Left and right inverses

• 3. Differentiation
3.1 The derivative
3.2 Optimization: necessity of vanishing derivative
3.3 Optimization: sufficiency in the convex case
3.4 An example of optimization in a function space

• 4. Geometry of inner product spaces
4.1 Inner product spaces
4.2 Orthogonal sets
4.3 Best approximation in a subspace
4.4 Fourier series
4.5 Riesz representation theorem
4.6 Adjoints of bounded operators

• 5. Compact operators
5.1 Compact operators
5.2 Approximation of compact operators
5.3 Appendix A: Bolzano-Weierstrass theorem
5.4 Appendix B: uniform boundedness principle

• Bibliography

• Index

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##### Worksheets (Solved)

###### Integration     