Distributions & Interpolation Spaces

Related lectures (28)

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Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the concept of distributions with compact support and their interpolation spaces.

Covers Green's representation formula, fundamental solutions, and distribution properties.

Covers probability distributions, moments, and continuous random variables.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Explores convolution operators, interpolation spaces, and function convergence in different spaces.

Explores the benefits of deeper networks in deep learning and the importance of over-parameterization and generalization.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.