I am looking for excellent VIDEO lectures on functional analysis. They should be
(1) in English (2) the video quality and voice is good (3) the lecture should not be presented in boring style
I am very thankful for your suggestions
2025-01-12 19:22:30.1736709750
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Video lectures on Functional Analysis
6.9k Views Asked by Abdulrahman Obaid https://math.techqa.club/user/abdulrahman-obaid/detail At
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I am also quite in search for good video lectures. The Nottingham ones posted by SamM are quite good but the problem, in my opinion, is that the course stays away from measure theory and so there is almost no discussion about $L^p$ spaces. The DTU ones posted by Giovanni are also very good, I think, but they don't do Weak$^*$ topology if I am right.
It is very hard to find a graduate level functional analysis class with video lectures I think.
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May I suggest another excellent online course ? I´ve watched most of the videos, and the teacher is very good, building proofs of many theorems.
01325 Mathematics 4 Real Analysis - dtu.dk
Normed vector spaces, Hilbert spaces, bases in Hilbert spaces, basic operator theory, the spaces L^p and l^p, approximation, the Fourier transform, convolution, the sampling theorem, B-splines, special basis functions (e.g, Legendre and Hermite polynomials), an introduction to wavelet theory.
http://www2.mat.dtu.dk/education/01325/ - course website
https://www.youtube.com/playlist?list=PLjRVZMfYBFMNp7IrHIMft5U_HIikp0T56 - YT
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There are two courses on Functional Analysis by a retired professor, S. Kesavan of The Institute of Mathematical Sciences, Chennai, India.
The first course is titled "Functional Analysis" and covers the following topics (in case the link gets deleted):
- Normed linear spaces, Continuous linear transformations, examples,
- Hahn-Banach theorem-extension form, Reflexivity
- Hahn-Banach theorem-geometric form, Vector-valued integration
- Baire’s theorem, Principle of uniform boundedness. Application to Fourier series, Open mapping, and closed graph theorems.
- Annihilators, Complemented subspaces, Unbounded operators, Adjoints.
- Weak topology. Weak-* topology, Banach-Alaoglu theorem, Reflexive spaces
- Separable spaces, Uniformly convex spaces, Applications to the calculus of variations
- $L^p$ spaces. Duality, Riesz representation theorem.
- $L^p$ spaces on Euclidean domains, Convolutions, Riesz representation theorem
- Hilbert spaces, Duality, Riesz representation theorem, Application to the calculus of variations, Lax-Milgram lemma, Orthonormal sets
- Bessel’s inequality, Orthonormal bases, Parseval identity, Abstract Fourier series, Spectrum of an operator
- Compact operators, Riesz-Fredholm theory, Spectrum of a compact operator, Spectrum of a compact self-adjoint operator
The second course is titled "Sobolev Spaces and Partial Differential Equations" and is yet to begin (at the time of writing this answer). The topics include:
- Test functions Distributions, calculus of distributions, support, and singular support of distributions.
- Convolutions of functions, Convolution of distributions, Fundamental Solutions.
- Fourier transform, Fourier inversion, Tempered distributions.
- Sobolev spaces, Definition, Approximation by smooth functions.
- Extension theorems, Poincare inequality, Imbedding theorems
- Compactness theorems, Trace theory.
- Variational problems in Hilbert spaces and Lax-Milgram lemma. Examples of weak formulations of elliptic boundary value problems.
- Regularity, Galerkin’s method, Maximum principles.
- Eigenvalue problems, Introduction to the finite element method.
- Semigroups of operators. Examples, Basic properties, Hille-Yosida theorem.
- Maximal dissipative operators, Regularity
- Heat equation, wave equation, Schrodinger equation. Inhomogeneous equations.
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https://youtube.com/playlist?list=PLmx4utxjUQD4xJkiHY4pp720LyeCZyEKW
A very engaging course taken by Prof.VittalRao(IISC)
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https://www.youtube.com/playlist?list=PLo4jXE-LdDTTIIIRwqK35CbFJieSJEcVR
The course given by Claudio Landim who is full professer of IMPA.
Check this one out: http://nptel.ac.in/courses/111105037/
It may be a bit slow but is extensive in content.