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1d
reviewed Approve suggested edit on When to learn category theory?
2d
comment Determine adjoint operator
No problem! $ $
2d
comment Determine adjoint operator
I guess what I meant was that you can write $L$ as $L(\phi)(x)=\int\chi_{\xi\leq x} K(x,\xi) d\xi$. So $L$ is an integral operator with kernel $(x,\xi)\mapsto\chi_{\xi\leq x} K(x,\xi)$. The adjoint $L^*$ has the same form, but with kernel $(y,\tau)\mapsto \chi_{y\leq \tau} K(\tau,y)$. Notice the swapped variables...
2d
comment Determine adjoint operator
Yes that's correct. (Btw, are you working with real-valued functions here? If complex, don't forget the conjugation of one of the argument functions in the scalar product!)
2d
comment Determine adjoint operator
No, the second double integral you wrote down does not make sense; the integral bound $x$ is meaningless. You can replace the integral from $0$ to $x$ by an integral over the whole space by adding an appropriate indicator function.
2d
comment Contraction Mapping, Metric
Just plug in the definitions of $d$ and $\tilde{}$ in $d(\tilde f,\tilde g)$ and see what you get!
2d
comment If $V$ is a $\mathbb CG$-module then we may take $\rho(g)$ as a diagonal matrix?
Related: math.stackexchange.com/questions/354926/…
2d
comment Compute limit $\lim_{n\rightarrow\infty}\frac{1*3*5*…*(2n-1) }{ 2*4*6*…*(2n)}=0$
Which limit do you want to compute? The one in the title or the one in the body of the question?
2d
answered Determine adjoint operator
2d
revised Contraction Mapping, Metric
added 206 characters in body
2d
answered Contraction Mapping, Metric
2d
comment Limit of an Indicator function
Which notion of convergence for functions are you considering?
2d
answered Does this identity involving limits hold?
Nov
10
revised Why locally compact hausdorff space
added 59 characters in body
Nov
9
awarded  Good Answer
Nov
5
comment cohomology of suspension
Cross post mathoverflow.net/questions/186243/cohomology-of-suspension
Nov
2
comment Set of vectors form a subspace of R3
It is a subspace.
Oct
31
comment Can we turn the functor “category ring” into a 2-functor in a natural way?
@Hurkyl: I think I'd rather restrict to categories with finitely many objects and have my rings have units.
Oct
26
comment We have $50$ numbers how many odd number are there in $50$ numbers
This is like asking: I have a number; is it even or odd?
Sep
30
awarded  Explainer