# Tagged Questions

The theory of functions of one complex variable with an emphasis on the theory of complex analytic (or holomorphic) functions of one complex variable. Typical topics include: Cauchy's integral formula, singularities, poles, meromorphic functions, Laurent and Taylor series, maximum modulus principle, ...

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### To prove ring properties of analytic functions

Let $R$ be the ring of entire functions $f: \mathbb{C} \rightarrow \mathbb{C}$ that are analytic at every point of $\mathbb{C}$ with respect to point-wise addition and multiplication. Then show that ...
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### Is there a meaningful measure on analytic functions?

Let $\mathcal{B}$ be the functions analytic on the unit disk and continuous on its boundary. With the supremum norm this becomes a Banach space. Is there any way to define a meaningful measure on ...
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### Flip integral boundaries of Delta function to get contradiction

Look at this equation: $\int_{-\infty}^{+\infty}dx\int_{-\infty}^{+\infty}dy\delta\left(x-y\right)f(y)=\int_{-\infty}^{+\infty}dxf(x)$ If I flip integration boundaries of both integrals, minus ...
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### Complex function $f$ is either constant or unbounded, but maximum value still does exist even if $f$ is not constant?

In Complex Variables and Applications, Brown & Churchill (9th edition), I stumbled upon a chapter which got me somewhat confused. On page 175 of the book, there is the theorem, which states the ...
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### $\int_0^\infty \frac{ x^{1/3}}{(x+a)(x+b)} dx$
$$\int_0^\infty \frac{ x^{1/3}}{(x+a)(x+b)} dx$$ where $a>b>0$ What shall I do? I have diffucty when I meet multi value function.