PSEUDOSPECTRA OF UNBOUNDED OPERATOR PENCILS

Abstract

This article investigates the (n, ϵ)-pseudospectrum of a closed operator pencil
and establishes various related properties, where ϵ > 0 and n ∈ Z+∪{0}. We reformulate the
heat equation as a non-self-adjoint 2×2 unbounded block operator matrix pencil. We derive
the spectral, pseudospectral, and (n, ϵ)-pseudospectral enclosures for 2×2 unbounded block
operator matrix pencil using the generalized Frobenius-Schur factorization. The results
obtained are then applied to determine the pseudospectral enclosure of the heat operator
pencil.