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

2 votes

$n$th root of $(a,b) \mapsto (\operatorname{gm}, \operatorname{am})$

A simple scheme (a parallel of which can be used to define the Gamma function from the factorial) is as follows: call $T$ your function, then define the functional square root as $$T^{\frac{1}{2}}=\l …
Yaakov Baruch's user avatar
3 votes

The missing link: an inequality

This is only a comment to @DimaPasechnik, but I cannot put the picture in a comment. The surface to the right of the $x=y$ is a plot of Dima's function (barring mistakes); clearly not convex.
Yaakov Baruch's user avatar
-1 votes

Is a function which is finitely multiple-valued in each variable separately, also finitely m...

Engineer a function that has n>=2 values exactly in the set $S_n \backslash S_{n+1}$ where $S_n$={(x,y) | x>n, y>n, (x-n)*(y-n)>1}, and 1 value elsewehere. That should work as a counterexample, as fa …
Yaakov Baruch's user avatar