Stone-Weierstrass Theorem

Related lectures (28)

Page 2 of 3

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores compact sets, extreme values, and function theorems on bounded sets.

Explores norm equivalence in complex functions, covering homogeneity and triangular inequality.

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

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

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

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