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Course11110614774 lectures

Functional Analysis

Prof. Kesavan · IMSc

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. 1.1: Normed Linear Spaces Video
  2. 1.2: Examples of Normed Linear Spaces Video
  3. 1.3: Examples, contd... Video
  4. 1.4: Continuous linear maps - Part 1 Video
  5. 1.5: Continuous linear maps - Part 2 Video
  6. 1.6: Isomorphisms Video

Week 2

  1. 2.1 - Exercises Video
  2. 2.2 - Exercises (contd.) Video
  3. 2.3 - Hahn-Banach Theorems Video
  4. 2.4 - Reflexivity Video
  5. 2.5 - Geometric version Video

Week 3

  1. 3.1 - Geometric version (contd.) Video
  2. 3.2 - Vector valued integration Video
  3. 3.3 - Exercises - Part 1 Video
  4. 3.4 - Exercises - Part 2 Video
  5. 3.5 - Baire's Theorem and Applications Video

Week 4

  1. 4.1 - Application to Fourier series Video
  2. 4.2 - Open mapping and closed graph theorems Video
  3. 4.3 - Annihilators Video
  4. 4.4 - Complemented subspaces Video
  5. 4.5 - Unbounded Operators, Adjoints - Part 1 Video
  6. 4.6 - Unbounded Operators, Adjoints - Part 2 Video

Week 5

  1. 5.1 - Orthogonality relations Video
  2. 5.2 - Exercises Video
  3. 5.3 - Exercises (contd.) Video
  4. 5.4 - Weak topology - Part 1 Video
  5. 5.5 - Weak topology - Part 2 Video
  6. 5.7 - Weak topology - Part 3 Video

Week 6

  1. 6.1 - Weak* topology - Part 1 Video
  2. 6.2 - Weak* topology - Part 2 Video
  3. 6.3 - Reflexive Spaces Video
  4. 6.4 - Separable Spaces - Part 1 Video
  5. 6.5 - Separable Spaces - Part 2 Video
  6. 6.6 - Uniformly Convex Spaces Video
  7. 6.7 - Applications Video

Week 7

  1. 7.1 - Exercises Video
  2. 7.2 - L-p Spaces - Part 1 Video
  3. 7.3 - L-p Spaces - Part 2 Video
  4. 7.4 - Completeness Video
  5. 7.5 -Duality Video
  6. 7.6 - L-p Spaces in Euclidean spaces - Part 1 Video
  7. 7.7 - L-p Spaces in Euclidean spaces - Part 2 Video

Week 8

  1. 8.1 - Dual of L-1 Video
  2. 8.2 - The space L-1 (contd.) Video
  3. 8.3 - Exercises - Part 1 Video
  4. 8.4 - Exercises - Part 2 Video
  5. 8.5 - Exercises - Part 3 Video
  6. 8.6 - Exercises - Part 4 Video

Week 9

  1. 9.1 - Hilbert spaces - Part 1 Video
  2. 9.2 - Hilbert spaces - Part 2 Video
  3. 9.3 - Duality Video
  4. 9.4 - Adjoints Video
  5. 9.5 - Applications Video
  6. 9.6 - Orthonormal sets Video

Week 10

  1. 10.1 - Orthonormal bases - Part 1 Video
  2. 10.2 - Orthonormal bases - Part 2 Video
  3. 10.3 -Fourier series Video
  4. 10.4 - Spectrum of an operator - Part 1 Video
  5. 10.5 - Spectrum of an operator - Part 2 Video
  6. 10.6 - Exercises - Part 1 Video

Week 11

  1. 11.1 - Exercises - Part 2 Video
  2. 11.2 - Exercises - Part 3 Video
  3. 11.3 - Compact operators - Part 1 Video
  4. 11.4 - Compact operators - Part 2 Video
  5. 11.5 - Riesz-Fredholm theory - Part 1 Video
  6. 11.6 -Riesz-Fredholm theory - Part 2 Video

Week 12

  1. 12.1 - Riesz-Fredholm theory Video
  2. 12.2 - Spectrum of a compact operator Video
  3. 12.3 - Spectrum of a compact self-adjoint operator Video
  4. 12.4 - Eigenvalues of a compact self-adjoint operator Video
  5. 12.5 - Exercises - Part 1 Video
  6. 12.6 - Exercises - Part 2 Video
  7. 12.7 - Exercises - Part 3 Video
  8. 12.8 - Exercises - Part 4 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IMSc
Department
Mathematics
Teacher
Prof. Kesavan
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
Who can watch
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