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2d
answered Explanation of $\overline{\lim} A_n$ and $\underline{\lim}A_n$
Jun
17
awarded  Yearling
Apr
19
awarded  Notable Question
Mar
3
answered Operator norm with $\inf$
Feb
20
comment Is $\lim_{x\to 0} (x)$ different from $dx$
Joseph, how do you define an infinitesimal? How do you define arithmetic operations on those? Now, do these definitions fit with the usual real numbers definitions? This should answer your question.
Feb
10
comment Applying Rouché's Theorem
I'm not talking about the whole polynomial. I'm talking about the $f$ you suggested, that is $f(z)=z^5+2z^4$, which has clearly a zero at $z=-2$.
Feb
9
revised Smoothness of a non-local functional
typos
Feb
8
answered Newton's method help
Feb
8
comment Enclosed Areas and Integration
Why do you have to solve for $x$? The integral is pretty straightforward with respect to $x$...
Feb
8
comment probability problem in an infinite continuous space
Could you tell us how you compute the probability in the second case? Also, I would not call it "infinite" continuous space, since we are in [0,1]...
Feb
5
comment Is this a bounded linear map?
Ah, you're right. I need to appeal to some variant of the AC in order to build it on the whole space, cause I can do it only on a dense subspace but then I need to extend it to the whole space. I deserve a -1 for this... Ok, now that we clarified this, I take back the fact that $Tx$ is always in $L^2$. However, as Nick showed, you can restrict $T$ to a subspace where you show that it is unbounded. That should be enough for you.
Feb
3
comment Is this a bounded linear map?
You can build many unbounded linear operators on Hilbert spaces. What does that have to do with the Axiom of Choice?
Feb
2
revised Tangential derivative vs covariant derivative
clarifying notation
Feb
2
comment Is this a bounded linear map?
I misunderstood your words: in your question it sounded to me like you were trying to find $x$ such that $Tx$ is not in $L^2$. What I meant in my answer was that the point is not whether or not $Tx$ is in $L^2$ for any choice of $x$ (and, in fact, it is), but rather that you cannot bound the norm of $Tx$ uniformly. Nick's answer show's one example of a family of functions $x_\varepsilon$ such that $||Tx_\varepsilon||/||x_\varepsilon||$ is not uniformly bounded with respect to the parameter $\varepsilon$.
Jan
26
answered Is this a bounded linear map?
Jan
26
asked Tangential derivative vs covariant derivative
Dec
10
revised Understanding weighted inner product and weighted norms
Write a statement more precisely
Nov
12
comment Absolute Maximum of the integral
Nice animation. What did you use to create it?
Oct
28
answered Low-rank matrix approximation in terms of entry-wise $L_1$ norm
Oct
28
comment Fractional Sobolev embedding into $L^\infty$
I don't understand the first inequality in the first line: how can you get rid of the absolute value of $e^{ix\cdot\xi}$ if you don't know that $\xi$ is real? For a general function, the F-transform may be defined for complex values of $\xi$. Am I missing something?