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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

40 votes
6 answers
5k views

Applications of Rademacher's Theorem

Rademacher's Theorem (that every Lipschitz function on $\mathbb{R}^{n}$ is almost everywhere differentiable) is a remarkable result on the structure of the space of Lipschitz functions, but I was wond …
Gordon Craig's user avatar
  • 1,665
18 votes
11 answers
4k views

Applications of measure, integration and Banach spaces to combinatorics

I'm going to be teaching a Master's level analysis course (measure theory, Lebesgue integration, Banach and Hilbert spaces, and if there's time, some spectral or PDE stuff) in the fall. My problem is …
Gordon Craig's user avatar
  • 1,665