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Results tagged with real-analysis
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user 123448
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
1
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A distribution $u$ such that all of its derivatives are of order zero is smooth
I'm reading Demailly's Complex Analytic and Differential Geometry In Section I.2.D.4 he uses the following fact: Suppose $u \in \mathcal{D}'(\Omega)$, where $\Omega \subset \mathbb{R}^n$ is a distribu …
- 1,141
3
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If subharmonic functions converge weakly to a subharmonic limit, why do their smoothings con...
Let $u_k$ be a sequence of subharmonic functions on an open set $X$ and $\psi_\delta$ a family of standard mollifiers with compact support. Hörmander claims in The Analysis of Linear Partial Different …
- 1,141
4
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smooth functions on closed intervals with values in infinite-dimensional spaces
There are three ways to define when a ($\mathbb{R}$-valued) function on a closed interval is smooth:
$f$ can be extended to a smooth function on $(a - \epsilon, b + \epsilon)$ for some $\epsilon > 0$ …
- 1,141