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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Is there a fixed-point index theorem that treats the fixed points on the boundary?
Suppose $f$ is a continuous function from a unit cube $[0,1]^n$ to itself, then $f$ has at least a fixed point. Further suppose $f$ is smooth, $0$ is a regular value of $f(x)-x$, and the fixed points …