二维拉普拉斯算子的比尔曼问题的显式求解

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI:10.1134/S1061920824030117

M. Malamud

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引用次数: 0

摘要

我们构建了一个二维拉普拉斯算子的适当限制，虽然其弗里德里希斯扩展的解析子并不紧凑，但却具有紧凑的前溶剂，而且其谱是绝对连续的。这一结果解决了比尔曼问题。 doi 10.1134/s1061920824030117

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Explicit Solution to the Birman Problem for the 2D-Laplace Operator

We construct an appropriate restriction of the 2-dimensional Laplace operator that has compact preresolvent though the resolvent of its Friedrichs extension is not compact and, moreover, its spectrum is absolutely continuous. This result solves the Birman problem.

DOI 10.1134/S1061920824030117

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.