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Fan Zheng's user avatar
Fan Zheng's user avatar
Fan Zheng
  • Member for 11 years, 5 months
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Distance function is unique nonnegative continuous function on $\mathbb{R}^d$ satisfying following
@Sean By definition there is a point $w$ in a neighborhood of $z$ such that $u(w) \le u(z) - (1 - \epsilon)|z - w|$. Let $r = u(x) - u(w)$.
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Fourier coefficients of real analytic functions on an n-dimension torus
@Ali That function is not well defined on the torus.
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Is there a name for this space?
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Existence of a function with slow growth on derivatives
Hint: Sobolev embedding.
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Existence of a function with slow growth on derivatives
That implies that the Taylor series of $f$ is convergent, i.e., $f$ is analytic, which cannot also be compactly supported.
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Solutions of a Diophantine equation with large common divisors
@Seva The 2-adic approach is not that easy, because I found $(x,y,u,v)=(222,10,6,14)$ satisfying your second equation mod $2^{18}$. This can then be Hensel lifted to a solution in 2-adic integers.
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Solutions of a Diophantine equation with large common divisors
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Existence of a viscosity solution
@AIM_BLB It is really curious to see a PDE with infinitely many independent variables. Could you shine a little bit more light on the background?
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