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| bio | website | maths.lth.se/matematiklth/… |
|---|---|---|
| location | Lund, Sweden | |
| age | 40 | |
| visits | member for | 1 year, 6 months |
| seen | 21 mins ago | |
| stats | profile views | 559 |
Associate professor, Lund University. Research interests: several complex variables, in particular pluripotential theory.
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5h |
comment |
complex analysis-roots of constant polynomial function Tou still mean "false" |
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11h |
comment |
$C_{c}(X)$ is a subspace of $C_{0}(X)$ but it is not Banach Also related: math.stackexchange.com/questions/284147 |
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1d |
answered | Continuity of the real and imaginary parts of a continuus complex-valued function |
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1d |
revised |
Function generation by input $y$ and $x$ values Fixed tags |
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1d |
comment |
Is this piecewise-defined function on $\mathbb{R}^2$ continuous at $(0,0)$? What about differentiable? Is the denominator correct? Are you sure it shouldn't be $x^2 + y^4$ (or some other combination involving both $x$ and $y$)? |
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2d |
revised |
Rouché Theorem to calculate the number of zeros Typo |
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2d |
comment |
Rouché Theorem to calculate the number of zeros $f$ has three zeros inside the circle. |
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2d |
comment |
Rouché Theorem to calculate the number of zeros @copper.hat You can formulate Rouché's theorem in several different ways. One common formulation (even Wikipedia's chosen one) is: if $|g| < |f|$ on $\partial\Omega$, then $f$ and $f+g$ have the same number of zeros on $\Omega$. |
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2d |
comment |
quick integration notation question I would guess that your interpretation is correct, but as already stated some context would be nice. |
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2d |
answered | Rouché Theorem to calculate the number of zeros |
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2d |
comment |
Rouché Theorem to calculate the number of zeros Within which domain? |
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2d |
comment |
Is it possible for a function to be analytic anywhere outside the circle of convergence of its power series expansion? From the comments above, now you can see why the phrasing is confusing. You need to think of $f$ and the power series of $f$ as separate entities. If you start with an analytic function on $\Omega$, you can compute its power series around any point $a\in\Omega$, but this series will only converge on a disc, not necessarily on the whole of $\Omega$. On the other hand, if you start with a power series, converging on some disc, it may very well have an analytic continuation to a larger domain. |
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2d |
comment |
Is it possible for a function to be analytic anywhere outside the circle of convergence of its power series expansion? Yes. At least with a suitable interpretation of what "non-analytic at least somewhere on the circle" means. |
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2d |
answered | Is it possible for a function to be analytic anywhere outside the circle of convergence of its power series expansion? |
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2d |
revised |
Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$ edited tags |
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2d |
answered | Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$ |
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May 21 |
revised |
Multiplication in $\mathcal D'(R)$. fixed typos |
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May 21 |
answered | Multiplication in $\mathcal D'(R)$. |
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May 20 |
answered | Show convergence for this sequence only by using the definition |
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May 20 |
comment |
Showing particular harmonic function is constant @BigTree Better? |
