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Results tagged with sp.spectral-theory
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user 153260
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
3
votes
Accepted
Leibniz rule for square root of Laplacian
For the Leibniz rule, it is not true that
\begin{equation} (-\Delta)^{\frac12}(fg) = f (-\Delta)^{\frac12}g + g (-\Delta)^{\frac12}f \end{equation}
even in the simplest possible case, i.e. in $\mathbb …
4
votes
Accepted
Is the spectrum of a "self adjoint" operator real on $\ell^p$?
It seems that I have found a counter example myself.
For the Hilbert matrix
$$ H_\lambda:= \big( \frac{1}{1-\lambda+k+n} \big)_{k,n\geq 0}, \lambda < 1 $$
Rosenblum in "On the Hilbert Matrix I, Pro …
11
votes
1
answer
465
views
Is the spectrum of a "self adjoint" operator real on $\ell^p$?
There might be an obvious answer to the question, but it doesn't come to mind.
Suppose we have an infinite matrix $A=(a_{ij})$, which defines a bounded linear operator on $\ell^p$, i.e. for all seque …