TY - JOUR
T1 - Generalized Airy operators
AU - Arnal, Antonio
AU - Siegl, Petr
N1 - Publisher Copyright:
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
PY - 2025/8/1
Y1 - 2025/8/1
N2 - We study the behaviour of the norm of the resolvent for non-self-adjoint operators of the form A:=−∂x+W(x), with W(x)≥0, defined in L2(R). We provide a sharp estimate for the norm of its resolvent operator, ∥(A−λ)−1∥, as the spectral parameter diverges (λ→+∞). Furthermore, we describe the C0-semigroup generated by −A and determine its norm. Finally, we discuss the applications of the results to the asymptotic description of pseudospectra of Schrödinger and damped wave operators, and also the optimality of abstract resolvent bounds based on Carleman-type estimates.
AB - We study the behaviour of the norm of the resolvent for non-self-adjoint operators of the form A:=−∂x+W(x), with W(x)≥0, defined in L2(R). We provide a sharp estimate for the norm of its resolvent operator, ∥(A−λ)−1∥, as the spectral parameter diverges (λ→+∞). Furthermore, we describe the C0-semigroup generated by −A and determine its norm. Finally, we discuss the applications of the results to the asymptotic description of pseudospectra of Schrödinger and damped wave operators, and also the optimality of abstract resolvent bounds based on Carleman-type estimates.
KW - complex Airy operator
KW - non-self-adjoint operator
KW - resolvent bounds
KW - resolvent operator
KW - Schrödinger operator
KW - spectral theory
UR - https://www.scopus.com/pages/publications/105012519870
U2 - 10.1017/prm.2025.10056
DO - 10.1017/prm.2025.10056
M3 - Article
AN - SCOPUS:105012519870
SN - 0308-2105
JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
ER -