A Blumenthal
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 Dec 26 awarded Yearling Dec 24 comment Ergodic means and Birkhoff theorem Does $\{ a\}$ refer to the fractional part of $a$? I ask because if so then the map you're interested in is en.wikipedia.org/wiki/Irrational_rotation on the unit circle, equipped with Lebesgue measure. Dec 24 answered evaluate the path integral around a circle in complex plane Dec 11 comment Show that every Banach space is isometric to a subspace of an $L_{\infty}(\mu)$-space math.stackexchange.com/questions/112619/… Jul 1 comment Preservation of Positive-Definiteness from Small Perturbations @the_elder It would be an interesting question (perhaps you should pose it!) to describe the geometry of the set of perturbations $B$ for which a given "strictly" positive semidefinite $A$ remains positive semidefinite. Jul 1 comment Preservation of Positive-Definiteness from Small Perturbations @the_elder No, if $A$ is "genuinely" semi-definite then it possesses a zero eigenvalue, hence a nontrivial kernel, and so is therefore noninvertible. In particular, there exist arbitrarily small perturbations $B$ which 'push' $A$ towards having negative eigenvalues. Jul 1 comment Preservation of Positive-Definiteness from Small Perturbations Hah, good catch @the_elder. $\Delta A$ must be hermitian itself before this result can possibly be true. Apr 6 reviewed Approve What does R^d in last lines refer to Jan 13 awarded Nice Question Jan 12 comment Integrate $\int_C{\tan{z}\ dz}; C: y=x^2$ (complex numbers) May you use the fact that the quotient of (non-vanishing) analytic functions is also analytic? Jan 8 revised Find the Fourier integral added 19 characters in body Jan 8 comment Find the Fourier integral Oops, I will correct the error. Jan 8 comment Find the Fourier integral @robjohn and my contour encircles precisely one of them. Jan 7 answered Find the Fourier integral Dec 26 awarded Yearling Dec 8 awarded Caucus Oct 24 reviewed Approve Area between curves $y=x^3$ and $y=x$ Oct 22 comment How to adapt the discrete-time to continuous, $(A) \Rightarrow (B)$? It is a standard and illuminating exercise to carry out this deduction for oneself. Hint: try applying the discrete-time MET to the time-one solution map. Does applying $d\phi^s_x$ for $s \in [0,1]$ affect the asymptotic growth rates of vectors? Oct 20 reviewed Approve Find Elements of a Quotient Group Oct 16 comment probability of clusters for iid points This is to say that the distribution of an $X_i$ depends on $n$ as well, correct? It would be more suggestive to write $X_i^{(n)}$, since you're really thinking of a triangular array of random variables.