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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
6
votes
Why is the Laplacian ubiquitous?
To build on what Andrey has mensioned about Brownian motion. The Laplacian is one of the points of connection between stochastic processes and analysis. The Laplacian appears as the infinitesimal gene …
6
votes
Fractal questions: Weierstraß-Mandelbrot
A quick, partial answer to your second question about the definition of fractals. If a fractal is generated by an iterated function system with a scaling ratio less than one then you do get a Hausdorf …