Reputation
755
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
3 14
Newest
 Yearling
Impact
~9k people reached

  • 0 posts edited
  • 0 helpful flags
  • 58 votes cast
Aug
24
awarded  Yearling
Jul
30
comment Compute the definite integral of f(x) as a limit of Riemann sums.
Make sure that each element in the sum is the area of a box: width $\times$ height. I suspect you do not multiply with the width of the box/interval ...
May
8
comment Analytic continuation in several variables
I think I understand. Could you please clarify the notation $\mathcal{O}(P_p)$? I am guessing it is the set of holomorphic functions with domain $P_p$?
May
8
comment Two self-adjoint operators with the same eigenvalues and eigenfunctions
In general, they are not, since the eigenfunctions may or may not form a basis for the Hilbert space.
May
8
comment Analytic continuation in several variables
Sorry, I hope it is clearer now.
May
8
revised Analytic continuation in several variables
added 108 characters in body
May
8
asked Analytic continuation in several variables
Apr
26
comment Is it mathematically valid to separate variables in a differential equation?
I would simply add an example. (I understand the question now.) It is a very good question, that deserves a good answer at this site.
Apr
26
comment Is it mathematically valid to separate variables in a differential equation?
It is not clear what kind of technique is referred to: "this separation" -- what separation? The quoted statement is without context.
Apr
26
comment Is it mathematically valid to separate variables in a differential equation?
This post does not contain enough information.
Apr
21
comment proving equation of an invertible matrix
Exactly: By using the assumption that $A$ is invertible, you produce a contradiction: the conclusion $X = Y$ contradicts that $X \neq Y$. So you have proved that the negation of your proposition is false.
Apr
21
comment proving equation of an invertible matrix
What happens if the opposite is true? If There is an $Y \neq X$, such that $AY = B$?
Mar
20
comment The function $f(z)=|z|^2$ is only differentiable at the origin
$f$ is complex differentiable if and only if the real and imaginary parts satisfy the Cauchy--Riemann equations.
Feb
17
comment Preimage of Legendre-Fenchel transform
In the non-convex case it is exactly the same. But I would rather have some more direct statements ..
Feb
17
comment Preimage of Legendre-Fenchel transform
Yes, I am interested in the case where $X$ may be nonreflexive, but also reflexive $X$ are of interest.
Feb
17
asked Preimage of Legendre-Fenchel transform
Feb
11
comment Prove that $f$ is identically zero.
Note that you can solve the differential equation: $df/f^2 = dx$. Integrate to get $f(x) = 1/[1/f(y) - (x-y)]$. for any $x,y$.
Jan
25
comment $\sum (\sqrt{x_k-k^2}-k)^2=0$ implies $x_k=2k^2$?
If you want to explore possible complex solutions, it may be fruitful to consider polar coordinate parameterizations of $X = x-1$ and $Y = y-4$, rewrite RHS as $(X+Y+5)/2$, and note that each square root has two branches ($X^{1/2} = |X|^{1/2}e^{i\theta + i k\pi})$, $k=0,1$), giving 4 possibilities on the LHS. I have no idea if you will find a solution, though.
Jan
24
comment $\sum (\sqrt{x_k-k^2}-k)^2=0$ implies $x_k=2k^2$?
I think the problem implicitly assumes that $x_k\geq k^2$. If ${x_k - k^2}<0$, you get two imaginary roots, and it is ambiguous which to choose from the notation. What is the context of this problem?
Jan
22
comment Questions about coerciveness and convexity
No, linear space means a set such that linear combinations of elements are in the set. Here, a linear combination of two functions is again a function. But this function may not be coercive!