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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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 …
40
votes
6
answers
5k
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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 …