NPTEL : NOC:Functional Analysis (Mathematics)

Co-ordinators : Prof. Kesavan


Lecture 1 - Normed Linear Spaces

Lecture 2 - Examples of Normed Linear Spaces

Lecture 3 - Examples (Continued...)

Lecture 4 - Continuous linear maps - Part 1

Lecture 5 - Continuous linear maps - Part 2

Lecture 6 - Isomorphisms

Lecture 7 - Exercises

Lecture 8 - Exercises (Continued...)

Lecture 9 - Hahn-Banach Theorems

Lecture 10 - Reflexivity

Lecture 11 - Geometric version

Lecture 12 - Geometric version (Continued...)

Lecture 13 - Vector valued integration

Lecture 14 - Exercises - Part 1

Lecture 15 - Exercises - Part 2

Lecture 16 - Baire's Theorem and Applications

Lecture 17 - Application to Fourier series

Lecture 18 - Open mapping and closed graph theorems

Lecture 19 - Annihilators

Lecture 20 - Complemented subspaces

Lecture 21 - Unbounded Operators, Adjoints - Part 1

Lecture 22 - Unbounded Operators, Adjoints - Part 2

Lecture 23 - Orthogonality relations

Lecture 24 - Exercises

Lecture 25 - Exercises (Continued...)

Lecture 26 - Weak topology - Part 1

Lecture 27 - Weak topology - Part 2

Lecture 28 - Weak topology - Part 3

Lecture 29 - Weak* topology - Part 1

Lecture 30 - Weak* topology - Part 2

Lecture 31 - Reflexive Spaces

Lecture 32 - Separable Spaces - Part 1

Lecture 33 - Separable Spaces - Part 2

Lecture 34 - Uniformly Convex Spaces

Lecture 35 - Applications

Lecture 36 - Exercises

Lecture 37 - L-p Spaces - Part 1

Lecture 38 - L-p Spaces - Part 2

Lecture 39 - Completeness

Lecture 40 - Duality

Lecture 41 - L-p Spaces in Euclidean spaces - Part 1

Lecture 42 - L-p Spaces in Euclidean spaces - Part 2

Lecture 43 - Dual of L-1

Lecture 44 - The space L-1 (Continued...)

Lecture 45 - Exercises - Part 1

Lecture 46 - Exercises - Part 2

Lecture 47 - Exercises - Part 3

Lecture 48 - Exercises - Part 4

Lecture 49 - Hilbert spaces - Part 1

Lecture 50 - Hilbert spaces - Part 2

Lecture 51 - Duality

Lecture 52 - Adjoints

Lecture 53 - Applications

Lecture 54 - Orthonormal sets

Lecture 55 - Orthonormal bases - Part 1

Lecture 56 - Orthonormal bases - Part 2

Lecture 57 - Fourier series

Lecture 58 - Spectrum of an operator - Part 1

Lecture 59 - Spectrum of an operator - Part 2

Lecture 60 - Exercises - Part 1

Lecture 61 - Exercises - Part 2

Lecture 62 - Exercises - Part 3

Lecture 63 - Compact operators - Part 1

Lecture 64 - Compact operators - Part 2

Lecture 65 - Riesz-Fredholm theory - Part 1

Lecture 66 - Riesz-Fredholm theory - Part 2

Lecture 67 - Riesz-Fredholm theory

Lecture 68 - Spectrum of a compact operator

Lecture 69 - Spectrum of a compact self-adjoint operator

Lecture 70 - Eigenvalues of a compact self-adjoint operator

Lecture 71 - Exercises - Part 1

Lecture 72 - Exercises - Part 2

Lecture 73 - Exercises - Part 3

Lecture 74 - Exercises - Part 4