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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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118 views

$\sup_{f} \inf_{z\in D} [f_x^2(z)+f_y^2(z)]$ for $|f|\leq1$ on a unit disk

Let $f:\mathbb{R^2}\mapsto\mathbb{R}$ be continuous and have partial derivatives in $D=\{(x,y):x^2+y^2\leq1\}$, and let $\mathscr{H}$ the set of such functions for which $\sup_D |f|\leq1$. Could some …
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A question about positive operator pregenerator [closed]

Thank you for reading. My question was raised up when I tried to prove an example in the book of Liggett(1985), which is in P13 Example 2.3(a). Here is a link of the page: https://books.google.com/ …
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