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1h
awarded  Constituent
1d
revised Is this a metric on matrices?
deleted 21 characters in body; edited title
Dec
8
awarded  Caucus
Dec
6
revised application of c*algebras to PDEs
edited title
Dec
3
revised Finding injection on natural numbers?
edited body
Dec
3
comment Finding injection on natural numbers?
Okay, then my answer will work. Notice that people think it's easy to inject $\mathbb N$ into $\mathbb N\times\mathbb N$ because the former is "smaller."
Dec
3
comment Finding injection on natural numbers?
Or are you actually looking for a bijection?
Dec
3
answered Finding injection on natural numbers?
Nov
26
reviewed Approve When to learn category theory?
Nov
25
comment Determine adjoint operator
No problem! $ $
Nov
25
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...
Nov
25
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!)
Nov
25
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.
Nov
25
comment Contraction Mapping, Metric
Just plug in the definitions of $d$ and $\tilde{}$ in $d(\tilde f,\tilde g)$ and see what you get!
Nov
25
comment If $V$ is a $\mathbb CG$-module then we may take $\rho(g)$ as a diagonal matrix?
Related: math.stackexchange.com/questions/354926/…
Nov
25
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?
Nov
25
answered Determine adjoint operator
Nov
25
revised Contraction Mapping, Metric
added 206 characters in body
Nov
25
answered Contraction Mapping, Metric
Nov
24
comment Limit of an Indicator function
Which notion of convergence for functions are you considering?