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A numerical investigation of the quadratic numerical range of Hain-Lüst operators

The quadratic numerical range (QNR) was introduced by Langer and Tretter [Spectral decomposition of some non-self-adjoint block operator matrices, J. Oper. Theory 39 (1998), pp. 339–359] as a tool for estimating the spectra of operators which admit a natural block matrix representation with respect to a decomposition of the underlying Hilbert space. We consider the problem of computing the QNR numerically for block differential operators, particularly these of Hain-Lüst type and Stokes type.