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On the numerical radius of operators in Lebesgue spaces
the numerical radius Lebesgue spaces
2010/11/24
We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|...
A Borg-Levinson theorem for higher order elliptic operators
A Borg-Levinson theorem elliptic operators
2010/11/15
We establish the Borg-Levinson theorem for elliptic operators of higher order with constant coefficients. The case of incomplete spectral data is also considered.