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Results tagged with pseudo-differential-operators
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user 18850
This tag is for questions regarding to the Pseudo-differential operator, acting on a space of functions on a differentiable manifold, that can locally be described by definite rules using a certain function. It satisfies estimates for the derivatives analogous to the estimates for derivatives of polynomials, which are symbols of differential operators.
6
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1
answer
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What is a good reference for conormal distributions?
May I humblely ask what is a good reference for conormal distributions (for student with some rudimentary pseudo-differential operator background)? I heard from my advisor that it is useful in index t …
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3
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Do Degree Zero Pseudo-Differential Operators on a Manifold Send Smooth Functions to Smooth F...
As Deane Yang pointed out, in general, an elliptic operator of order $s$ maps $H^{k}\rightarrow H^{k-s}$ for functions defined on $\mathbb{R}^{n}$. The pseudo-differential operator on a compact manifo …
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1
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Accessible reference for (scattering) $\Psi DO$'s on manifolds
I take a very brief look at the paper and I did not see $\Psi DO$ on manifold with boundary being used heavily anywhere (no conormal distribution, multiple blow-ups, heavy handed symbol estimates, etc …
1
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0
answers
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Bound of analytic torsion for a line bundle
Let $E\rightarrow X$ be a line bundle over a compact Riemann surface. Let $\Delta_{E}$ be the Dolbeault Laplacian $\Delta_{\overline{\partial}}$ extended to sections of $E$. Let $g_1, g_2$ be two metr …
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1
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K-homology classes of Dirac operators on Hermitian manifolds
I am not entirely familiar with $KK$-theory, so please correct me if there are mistakes. I think ultimately you are trying to show the topological $K$-theory class you get from taking the horizontal d …
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3
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BVPs for elliptic PDOs: When do Green functions ($L^2$ inverses) define pseudo-differential ...
The book by Melrose was almost exactly written to address issues like the ones you mentioned above, where the very first example is the one in the question. The construction fo the parametrix is the f …
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