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 Apr 5 asked Infinite dimensional Hamiltonian systems: looking for textbook/general results Dec 27 accepted Discontinuous functionals on $L^p$ Sep 24 awarded Popular Question Sep 19 answered Relationship between spherical volume and rectangular volume Aug 24 awarded Yearling May 8 comment Analytic continuation in several variables I think I understand. Could you please clarify the notation $\mathcal{O}(P_p)$? I am guessing it is the set of holomorphic functions with domain $P_p$? May 8 comment Two self-adjoint operators with the same eigenvalues and eigenfunctions In general, they are not, since the eigenfunctions may or may not form a basis for the Hilbert space. May 8 comment Analytic continuation in several variables Sorry, I hope it is clearer now. May 8 revised Analytic continuation in several variables added 108 characters in body May 8 asked Analytic continuation in several variables Apr 26 comment Is it mathematically valid to separate variables in a differential equation? I would simply add an example. (I understand the question now.) It is a very good question, that deserves a good answer at this site. Apr 26 comment Is it mathematically valid to separate variables in a differential equation? It is not clear what kind of technique is referred to: "this separation" -- what separation? The quoted statement is without context. Apr 26 comment Is it mathematically valid to separate variables in a differential equation? This post does not contain enough information. Apr 21 comment proving equation of an invertible matrix Exactly: By using the assumption that $A$ is invertible, you produce a contradiction: the conclusion $X = Y$ contradicts that $X \neq Y$. So you have proved that the negation of your proposition is false. Apr 21 comment proving equation of an invertible matrix What happens if the opposite is true? If There is an $Y \neq X$, such that $AY = B$? Mar 20 comment The function $f(z)=|z|^2$ is only differentiable at the origin $f$ is complex differentiable if and only if the real and imaginary parts satisfy the Cauchy--Riemann equations. Feb 17 comment Preimage of Legendre-Fenchel transform In the non-convex case it is exactly the same. But I would rather have some more direct statements .. Feb 17 comment Preimage of Legendre-Fenchel transform Yes, I am interested in the case where $X$ may be nonreflexive, but also reflexive $X$ are of interest. Feb 17 asked Preimage of Legendre-Fenchel transform Feb 11 comment Prove that $f$ is identically zero. Note that you can solve the differential equation: $df/f^2 = dx$. Integrate to get $f(x) = 1/[1/f(y) - (x-y)]$. for any $x,y$.