Approximation by Smooth Functions

Related lectures (28)

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

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers weak derivatives, their properties, and applications in functional analysis.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.