Titlebook: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations; Johannes Sjöstrand Book 2019 Springer Nature Switz

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Capitulate

Pseudo-Differential Operatorshttp://image.papertrans.cn/n/image/667022.jpg

背信

defile

贝雷帽

Quasi-Modes in Higher Dimensionhe same domain given by . Here . denotes the Hamilton vector field of .. The following result is due to Zworski, who obtained it via a semi-classical reduction from the above mentioned result of Hörmander. A direct proof was given in Dencker et al. and here we give a variant. We will assume some familiarity with symplectic geometry.

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exhilaration

Counting Zeros of Holomorphic Functionsand (Math Ann 342(1):177–243, 2008. .) we obtained such a generalization, by weakening the regularity assumptions on the functions .. However, due to some logarithmic losses, we were not quite able to recover Hager’s original result, and we still had a fixed domain Γ with smooth boundary.

偶然

Perturbations of Jordan Blocksmall (random) perturbation of .. we expect the eigenvalues to move inside a small neighborhood of .. In the special case when . = (.|..).., where . is the canonical basis in .., we have seen in Sect. . that the eigenvalues of .. are of the form . so if we fix 0 < . ≪ 1 and let . →., the spectrum “will converge to a uniform distribution on ..”.

CAMEO

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