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Apr
7
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Feb
18
awarded  Popular Question
Dec
12
comment Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
@user123 assume $f$ is nonconstant, holomorphic on $D$ and continuous on $\bar{D}$, with $f$ nonvanishing on $D$, ... then use the minimum modulus principle we effectively just showed in the previous problem to get a contradiction
Dec
12
comment Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
@user123 The maximum of $f$ on the closure of $D$ is the maximum on the boundary by the maximum modulus principle, and because $\bar{D}$ is compact. Comsidering $g=1/f$, we see $g$ has the same property, and hence $f$ attains both its maximum and minimum on the boundary. Since $f$ is constant there, by the open mapping theorem, we have $f$ is constant.
Oct
29
accepted On the dual face of a subset of a convex cone
Oct
29
comment On the dual face of a subset of a convex cone
It's the third dual of $F$. And now that you mention it, I think it follows from the definition. My bad.
Oct
29
revised On the dual face of a subset of a convex cone
added details
Oct
29
revised On the dual face of a subset of a convex cone
typo
Oct
29
asked On the dual face of a subset of a convex cone
Oct
26
accepted On the range of positive semidefinite matrices
Oct
26
asked On the range of positive semidefinite matrices
Oct
15
awarded  Popular Question
Oct
8
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Oct
7
awarded  Yearling
Jul
20
awarded  Notable Question
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11
awarded  Notable Question
Jun
4
revised Estimate for the power of a integral
added information
Jun
4
answered Estimate for the power of a integral
May
17
awarded  Nice Question
Apr
10
accepted On closed ranges and sequences which converge to zero