Abstract
We study one-dimensional Schrödinger operators H=−∂x2+V with unbounded complex potentials V and derive asymptotic estimates for the norm of the resolvent, Ψ(λ):=‖(H−λ)−1‖, as |λ|→+∞, separately considering λ∈RanV and λ∈R+. In each case, our analysis yields an exact leading order term and an explicit remainder for Ψ(λ) and we show these estimates to be optimal. We also discuss several extensions of the main results, their interrelation with some aspects of semigroup theory and illustrate them with examples.
Original language | English |
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Article number | 109856 |
Journal | Journal of Functional Analysis |
Volume | 284 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1 May 2023 |
Keywords
- Complex potential
- Pseudospectrum
- Resolvent estimate
- Schrödinger operator
ASJC Scopus subject areas
- Analysis