Metafune, G.; Sobajima, M.; Spina, C. Spectral properties of operators obtained by localization methods. (English) Zbl 1356.47052 Note Mat. 35, No. 1, 67-74 (2015). Summary: We prove that, given two elliptic operators \(A_{1}\) and \(A_{2}\) in \(L^p(\Omega_{1})\) and \(L^p(\Omega_{2})\) respectively whose spectral properties are known, we can deduce those of the operator \(A\) coinciding with \(A_{1}\) on \(\Omega_{1}\) and with \(A_{2}\) on \(\Omega_{2}\). Conversely, if the spectral properties of the operator \(A\) are known in \(L^p(\Omega)\), we deduce those of the restriction of \(A\) to a smaller subset of \(\Omega\). Cited in 2 Documents MSC: 47F05 General theory of partial differential operators 47A10 Spectrum, resolvent 47D06 One-parameter semigroups and linear evolution equations 35J99 Elliptic equations and elliptic systems Keywords:elliptic operators; resolvent estimates; analytic semigroups PDFBibTeX XMLCite \textit{G. Metafune} et al., Note Mat. 35, No. 1, 67--74 (2015; Zbl 1356.47052) Full Text: DOI