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1d

comment 
compact inclusion of domains of unbounded operators
How do we know that $\mathcal{D}(L^{1/2}) \subset H^{1/2}$? It isn't obvious to me. 
1d

comment 
compact inclusion of domains of unbounded operators
Are $\mathcal{D}(L)$, $\mathcal{D}(L^{1/2})$ equipped with their graph norms, or something else? 
1d

revised 
CohenMacaulay rings and Normal rings
typo in title 
Apr 21 
answered  Existence of a measurepreserving bijection 
Apr 21 
comment 
Functional minimization problem
@RyanBudney: Maybe $k$ is supposed to be fixed? 
Apr 21 
comment 
Real and imaginary part of an holomorphic function
What is your definition of "holomorphic function"? 
Apr 20 
comment 
What is the mathematical structure called if we replace commutative group by commutative monoid in the definition of linear space?
Based on your comments, maybe the term you are looking for is simply "cone", which is a subset of a (real or complex) vector space that is closed under addition and under multiplication by nonnegative scalars. 
Apr 16 
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Rate of convergence in the Law of Large Numbers
Related to your other questions: mathoverflow.net/questions/73647/… 
Apr 16 
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Rate of convergence in the Law of Large Numbers
I don't know an exact reference either, but I suspect that with a little work you can show that a distribution satisfying $EX^\alpha < \infty$ will satisfy the KG hypotheses. 
Apr 16 
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Rate of convergence in the Law of Large Numbers
Right. In the infinite second moment case, by "CLTtype result" I'm talking about a KolmogorovGnedenko style stable law limit theorem giving the weak convergence of $(S_n  \mu n)/n^{1/\alpha}$ (typically the weak limit is a stable law, not the normal distribution). 
Apr 16 
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Rate of convergence in the Law of Large Numbers
Maybe I'm confused, but doesn't a CLTtype result give you exactly what you want? In the finitevariance case, the classical CLT says that $(S_n  \mu n)/n^{1/2}$ converges weakly, so as a result $E_n/n^{1/2 + \epsilon} \to 0$ weakly and hence in probability (standard result). So a CLTtype result telling you that $(S_n  \mu n)/ n^{1/\alpha}$ converges in distribution would imply that $E_n / n^{1/\alpha + \epsilon} \to 0$ in probability. 
Apr 15 
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Area enclosed by Brownian motion (without winding number)
@CarloBeenakker: Hmm, and I actually voted on that question. Seems that my memory doesn't last more than 2 years. Well, it got only a very partial answer there, maybe we will learn more from the MO crowd. 
Apr 15 
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Lower order perturbations of 2nd order differential operators
Thinking in terms of spectra, selfadjoint operators tend to behave like real numbers, and skewadjoint operators are imaginary numbers. It's a little like asking "if I take a real number, and add a very small imaginary number, might the result turn out to be real?" No, it never will. 
Apr 15 
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Lower order perturbations of 2nd order differential operators
The problem is more fundamental than that. In KatoRellich the perturbation is at least symmetric, and the problem is to sort out the domain of the adjoint. An example is something like a second order operator perturbed by a zero order term. Here your perturbation is not even symmetric: integration by parts suggests that formally $(\beta X)^* = \beta X + V$ for some zeroorder term (potential) $V$. It's more likely to be skew symmetric. 
Apr 14 
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Lower order perturbations of 2nd order differential operators
As an analogy in the elliptic setting, $P = d^2/dx^2$ is selfadjoint on $L^2(\mathbb{R}, dx)$ but $Q = d^2/dx^2 + d/dx$ is not (its adjoint is $d^2/dx^2  d/dx$). However, $Q$ is selfadjoint on $L^2(\mathbb{R}, e^{x} dx)$. 
Apr 14 
comment 
Lower order perturbations of 2nd order differential operators
Typically, not unless you change the measure in just the right way. Almost anything you try will be a counterexample. 
Apr 14 
revised 
Area enclosed by Brownian motion (without winding number)
in distribution 
Apr 14 
asked  Area enclosed by Brownian motion (without winding number) 
Apr 13 
answered  Diffusion semigroup generated by Laplacian 
Apr 13 
revised 
SDEs: Bounding the variance of a solution
added 192 characters in body 