Kofi
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Registered User
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3h |
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Dirac measures dense in space of measures? What an easy argument! Thanks! |
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5h |
asked | Dirac measures dense in space of measures? |
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1d |
revised |
The first eigenvalue of the Schrödinger operator is simple. deleted 2 characters in body; edited body; added 20 characters in body |
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1d |
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The first eigenvalue of the Schrödinger operator is simple. The argument in the last paragraph also works with $C^2$ instead of $C^\infty$, and the solutions are always $C^2$. You should check out some book about PDE (e.g. the mentioned one by Evans or Gilbarg-Trudinger) to get the exact statements about regularity (especially at the border), but in principle, the same argument should work in most related cases. |
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2d |
answered | The first eigenvalue of the Schrödinger operator is simple. |
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May 16 |
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Special kind of operators Thank You for the reference. It turned out, such an operator is (2,1,2) nuclear. |
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May 15 |
asked | Special kind of operators |
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May 14 |
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Absolutely 2-summable operator on a Hilbert space Wow, that is really interesting! Thank you for your answer! |
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May 13 |
asked | Absolutely 2-summable operator on a Hilbert space |
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May 13 |
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Triangle area on surfaces of constant curvature I don't understand what you mean. I have a Riemannian metric of constant curvature on a Surface. This gives me curvature and a volume density, so I know both what curvature and area is and I can in theory calculate what the area of a geodesic triangle is. Where do I need an axiom? |
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May 12 |
asked | Triangle area on surfaces of constant curvature |
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May 9 |
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Fourier transform of a bounded function I suppose, continuity of the function does not help either? |
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May 9 |
asked | Fourier transform of a bounded function |
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May 5 |
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zeta(3) in terms of derivatives of zeta at 1/2 and pi What do you mean with "the last equality holds to precision 10^-4"? If the result was true, shouldn't the equality hold up to any precision? |
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May 2 |
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Gap between first two nonzero Laplacian eigenvalues on closed compact surface? Probably one should skip the "nonzero" requirement as in this case, the gap is always positive. |
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Apr 28 |
answered | Linearization of vector fields |
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Apr 17 |
asked | Heat Kernel Asymptotics with low regularity |
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Mar 31 |
asked | Difference between parallel transport and derivative of the exponential map |
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Mar 22 |
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sections of tensor product bundle ( tensor product of two vector bundles ) First, how is your actual question related to connections? Secondly, on any bundle, you can construct a section by patching it together locally with partitions of unity! |
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Feb 26 |
revised |
Heat Kernel Asymptotics on Manifold with Boundary added 255 characters in body; added 4 characters in body; deleted 39 characters in body |
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Feb 26 |
asked | Heat Kernel Asymptotics on Manifold with Boundary |
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Feb 26 |
awarded | ● Popular Question |
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Feb 7 |
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From Topological to Smooth and Holomorphic Vector Bundles I think what you want to hear in relation to (C) is the word "Thom isomorphism" |
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Jan 17 |
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About writing of mathematical papers I almost never use $\Longrightarrow$, $\exists$ or $\forall$. |
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Jan 14 |
asked | Asymptotic Expansion of the Schrödinger kernel? |
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Jan 8 |
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Trace formula for PSDOs Can you elaborate on this? I don't really know what to make of it. |
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Jan 7 |
asked | Trace formula for PSDOs |
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Jan 2 |
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Solution of a PDE and its uniqueness I may be wrong, but at first sight I would say this looks pretty hopeless to answer. |
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Dec 29 |
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Math for a cake This should be two, not zero, shouldn't it? |
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Dec 19 |
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Excellent mathematical explanations I think that whether a proof is explanatory is highly individual and depends on the knowledge you already have. Some people may be satisfied with some argument while others still don't have a feeling of understanding. |
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Dec 13 |
asked | Heat kernel proof of Poincaré Hopf |
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Dec 9 |
revised |
Combinatorics: Product Rules. deleted 10 characters in body |
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Dec 8 |
asked | Combinatorics: Product Rules. |
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Dec 5 |
asked | Index theorems and orientability |
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Dec 2 |
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Fourier Transform, for entire function Your statement about defining the Fourier transform by duality does not make sense... As you pointed out yourself, the fourier transform of a function in D is not in D again, but in S. Hence taking the dual operator gives again only an operator from S' to D'. |
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Dec 2 |
answered | Fourier Transform, for entire function |
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Dec 1 |
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What are the Dirac operators on $S^1$? Hopefully, my answer at stackexchange is answering your question. |
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Dec 1 |
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An invariant method of stationary phase So the constant depends on $t$? |
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Nov 28 |
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An invariant method of stationary phase Yes, this is basically what I wrote in my edit to the above post, except that I considered the real case (I think the $e^{it\psi(x)}$ is wrong in your definition of $c$?). But the higher coefficients always make use of a chart. |
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Nov 27 |
revised |
An invariant method of stationary phase added 2 characters in body; added 2 characters in body |
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Nov 27 |
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An invariant method of stationary phase Yes, this is the standard way. It works just as well in the case that $\phi$ is purely real (and gets even simpler). However, it describes the asymptotic expansion via differential operators given in Morse coordinates. And there is a vast amount of Morse coordinates for a given function. Of course, the term cannot depend on this choice, however when looking at its definition, this is not obvious at all. I am looking for a description of these terms such that one can see their invariance of the choice of Morse chart by its definition. |
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Nov 27 |
revised |
An invariant method of stationary phase added 37 characters in body |
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Nov 27 |
revised |
An invariant method of stationary phase added 736 characters in body |
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Nov 27 |
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An invariant method of stationary phase I know the statement in Duistermaat, and I know that one can determine the sj more specifically using local coordinates. In fact, it is just a Laplacian when using Morse coordinates. However, it should be possible to figure out the $s_j$ without using any coordinates, just by using invariance theory. |
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Nov 27 |
asked | An invariant method of stationary phase |
