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Results tagged with cv.complex-variables
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user 37087
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
7
votes
2
answers
3k
views
An extension of Morera's Theorem
Morera's Theorem states that
If $f$ is continuous in a region $D$ and satisfies $\oint_{\gamma} f = 0$ for
any closed curve $\gamma$ in $D$, then $f$ is analytic in $D$.
I have two questions: …
- 398
1
vote
1
answer
526
views
Stone-Weierstrass Theorem, polynomial interpolation, divided difference in complex plane
Setting:
Let $\Gamma$ be a simple smooth($C^\infty$) curve in $\mathbb{C}$ parametrized by the injective map $\gamma:[0,1] \to \mathbb{C}$.
Assume $f$ is a function defined on $\Gamma$ s.t. $f$ is su …
- 398
4
votes
1
answer
1k
views
upper bound on derivatives of a function defined on an arc
This is a simple question I asked in math.SE last month but unfortunately no one gives any comment. So I decided to try some luck here.
You can skip examples below and read from "General setting" at t …
- 398