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Patch
  • Member for 11 years, 8 months
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  • Baltimore, MD, United States
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using the M. Riesz Interpolation Theorem
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Looking for some "nontrivial" examples of pseudodifferential operators/symbols
@DeaneYang What "section" are you referencing? Also, can you give an explicit example? Maybe a worked parametrix with specific coefficients?
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Fourier transform of compactly supported distribution is smooth
Thanks, everyone. It's nice to know that I wasn't just missing something trivial. This is a good theorem to know!
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using the M. Riesz Interpolation Theorem
The value $p=4$ might not be special, but it is the only instance in which we are able to prove the $\limsup$ convergence explicitly.
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using the M. Riesz Interpolation Theorem
Oh, of course! Sorry. Thanks again.
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using the M. Riesz Interpolation Theorem
Thanks. That really helps. This is the [Hölder interpolation][1] theorem you're referencing, correct? In the case when $p_t\in(4,6)$ though, we end up with $$\lambda_k^{-\delta(p_t)}||e_{\lambda_k}||_{p_t} \leq \left( \lambda_k^{-\delta(4)}||e_{\lambda_k}||_4 \right)^{1-t}\left( \lambda_k^{-\delta(6)}||e_{\lambda_k}||_6 \right)^{t}$$ and we can no longer rely on the unit-norm in $L^{2}(M)$ nor the fact that $\delta(2)=0$. How do we proceed from here? [1]: en.wikipedia.org/wiki/…
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