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comment derivative of a linear operator
thank you guys. This is from Zeidler's applied functional analysis. I imagine there is an errata somewhere...
Jul
8
comment Can I show that a process which a supermartingale above a certain value and a submartingale below it converges?
Limit must exists by martingale convergence theorem. The limit is almost sure and $L^1$
Jul
8
comment Are $n$-dimension cubes $C^k$ manifolds with boundaries?
@AlexS can you just confirm for me that my understanding for boundary is correct.
Jul
8
comment Are $n$-dimension cubes $C^k$ manifolds with boundaries?
@AlexS can you please provide me with a reference. My source is Wikipedia: en.wikipedia.org/wiki/…
Jul
8
comment Definition of $C^k$ boundary
just to check: a square is does not have a $C^1$ boundary because of at the corners?
Jul
7
comment Continuous Sobolev Embedding
@Ian yeah that is what I thought - thanks a bunch, but only on a finite domain?
Jul
7
comment Continuous Sobolev Embedding
I want to know if $W^{k,p}$ goes into $W^{l,q^*}$, what does that say about $W^{k,p}$ goes into $W^{l,q}$ for $1\leq q \leq q^*$ also does this hold for say $L^p$ and $W^m,p$?
Jul
7
comment Continuous Sobolev Embedding
@Ian what if the differentiability order is not 1? (I only need a bounded domain, but what about in general?)
Jul
7
comment Continuous Sobolev Embedding
Can you please elaborate on the relationship to Sobolev embedding theorem and confirm what I said in the comment for the question is correct?
Jul
7
comment Continuous Sobolev Embedding
@Ian woah, let me digest that. Do you mean for a particular $W^{m,p}$, say, for a fixed $n$, smaller than the particular $1\leq q\leq q^*$ the embedding is continuous? (where q^* is given by the Sobolev embedding theorem)
Jun
26
comment Expectation value of number of drawings of increasing sequences of labelled balls from an urn.
@uomoinverde if you think the reasoning is sound, then I am pretty sure that one can rearrange what I have written into your formula, but you did not want to do it... otherwise it is wrong.
Jun
22
comment Expectation value of number of drawings of increasing sequences of labelled balls from an urn.
Your approach 2 is right, whether it results in an explicit formula, I do not know. why do you think your conjecture is correct?, surely to arrive at that formula, you used some counting argument? also where does the problem come from?
Jun
18
comment Computing $\lim \limits_{n\to \infty}Pr(X_n=0)$ for r.v $X_n$ using matrices and Markov Chains.
The matrix limit will tend to a limiting matrix $\Pi$ such that each row of $\Pi$ is just $\pi$... and oh the limit is independent of where you start...
Jun
18
comment Computing $\lim \limits_{n\to \infty}Pr(X_n=0)$ for r.v $X_n$ using matrices and Markov Chains.
@Meitar that is certainly easier than calculating matrix exponentials... Note that $\pi^T$ is just the eigenvector of $P^T$ with eigenvalue 1 and the entries adds up to one. Perron-Frobenius theorem says the dimension of the eigenspace is 1, so there will only be a unqiue one.
Jun
9
comment Can a monotone decreasing function intersect $y=-x$ on a set of more than measure $0$?
Ah, i see, i did not know what one of those was. Thanks again
Jun
9
comment Can a monotone decreasing function intersect $y=-x$ on a set of more than measure $0$?
@DanielFischer but doesnt the cantor set have measure 0?
Jun
9
comment Can a monotone decreasing function intersect $y=-x$ on a set of more than measure $0$?
@DanielFischer urgh... Thanks
Jun
9
comment Lagrangian multiplier vectorial form
$h(x)$ is vector, if that helps...
Jun
1
comment Regularity of PDE with respect to coefficients?
@HomegrownTomato do you know if it is a problem if the boundary condition also depends on sigma. (and the notes looks dense! I think it will serve as a good starting point to find something which assumes less)
May
31
comment Regularity of PDE with respect to coefficients?
@Ian do you have anything to suggest which may help me to answer prove what i said is true in the example i gave?