论文标题
广义通风运营商
Generalised Airy Operators
论文作者
论文摘要
我们研究了$ a：= - \ partial_x + w（x）$的非自身辅助操作员的分解规范的行为，带有$ w（x）\ ge 0 $，定义为$ l^2（\ mathbb {r}）$。我们对其解决方案操作员的规范提供了详尽的估计，$ \ | （a-λ）^{ - 1} \ | $，因为频谱参数差异$（λ\ to +\ infty）$。此外，我们描述了由$ -A $生成的$ C_0 $ -Semigroup并确定其标准。最后，我们讨论了结果对Schrödinger和Damped Wave Operators伪斑的渐近描述的应用，以及基于Carleman型估计值的抽象分辨率界限的最佳性。
We study the behaviour of the norm of the resolvent for non-self-adjoint operators of the form $A := -\partial_x + W(x)$, with $W(x) \ge 0$, defined in $L^2(\mathbb{R})$. We provide a sharp estimate for the norm of its resolvent operator, $\| (A - λ)^{-1} \|$, as the spectral parameter diverges $(λ\to +\infty)$. Furthermore, we describe the $C_0$-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.
