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Jan
22
comment Intuitive Aproach of Dolbeault Cohomology
If, by intuitive, you mean "geometrical", i.e. related to things like submanifolds and boundaries, I don't think you will find one. $H^{p,q}$, in general, has no interpretation in terms of geometry of submanifolds or such ...
Jan
13
comment Show that a function has essential singularity
I elaborated further on the first limit...
Jan
13
revised Show that a function has essential singularity
Added explanation of the first limit.
Jan
11
answered Show that a function has essential singularity
Jan
8
answered In the real spherical harmonics, where does the sqrt(2) factor come from?
Dec
30
answered Why do complex eigenvalues correspond to a rotation of the vector?
Dec
30
comment Lines of Level Curves of an Analytic Function's Real and Imaninary Parts
And similarly for the imaginary part, only with $\mathrm{Im}\zeta^2=0$ which is $xy=0$.
Dec
30
comment Lines of Level Curves of an Analytic Function's Real and Imaninary Parts
What I am saying is that a neighbourhood of $z_0$ in the set you want to study is conformally mapped onto a neighbourhood of $(0,0)$ in $x^2-y^2=0$ ... the set which is union of two perpendicular lines is $\{\zeta\in W\ :\ \mathrm{Re}\;\zeta^2=0\}$ which, if $\zeta=x+iy$, is given by the equation $x^2=y^2$ ...
Dec
30
answered Lines of Level Curves of an Analytic Function's Real and Imaninary Parts
Dec
30
revised Show that all derivatives of $f(x) = \frac{\sin(2\pi x)}{\pi x}$ belong to $L^2(\mathbb{R})$
added 53 characters in body
Dec
30
answered Show that all derivatives of $f(x) = \frac{\sin(2\pi x)}{\pi x}$ belong to $L^2(\mathbb{R})$
Dec
13
comment Mistake in reasoning: $Pv\frac{1}{x} = 0$??
$f(\epsilon)\leq \|\phi\|\left(\left|\int_{-a}^{-\epsilon}\frac{1}{x}dx\right|+\left|\int_{\epsil‌​on}^{a} \frac{1}{x}dx\right|\right)$ which tends to infinity as $\epsilon$ goes to $0$. You cannot take the sup norm out of the integral without also taking some absolute value along the way...
Dec
9
comment Two generating meromorphic functions seperate points on a compact Riemann surface?
You can choose $h$ such that $h(p)\neq h(q)$ and none of them is $\infty$ (just change coordinate on $\mathbb{CP}^1$)... then, if $\beta(z)=0$, it means that also $\alpha(z,f)=0$ ...
Dec
9
comment Decomposition of analytic functions
Sorry, I haven't got back at you because I really have no clue on how to do it for two generic open connected sets ... if you don't have any particular geometric structure (like in your example with annuli) I don't really see how some "global" results like the ones you mentioned could be of use...
Dec
4
awarded  Yearling
Dec
4
comment Continuity is required for differentiability?
Sorry, but $f(x)=1/x$ and $f(x)=1/x^2$ are not differentiable in $0$, which is also the point where they are not continuous... so what are you asking, exactly?
Dec
4
answered Why the map $z→z+ \overline z^m $ has fixed point with local Lefschetz number $m$ at the the origin of C (m≥0)?
Dec
4
revised Proof of holomorphic Lefschetz fixed point formula using currents in Griffiths and Harris
added 342 characters in body
Dec
4
answered Proof of holomorphic Lefschetz fixed point formula using currents in Griffiths and Harris
Nov
28
comment Decomposition of analytic functions
Was this given to you as an exercise in such a course? If so, what were the topics treated just before?