从零点分解展开到长时波展开

arXiv - MATH - Spectral Theory Pub Date : 2024-08-06 DOI:arxiv-2408.03234

T. J. Christiansen, K. Datchev, M. Yang

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引用次数: 0

摘要

我们证明了一个一般性的抽象定理，即在高能量时，在多项式有界的假设下，从能量为零时的解析展开推导出时间为无限时的波展开。我们给出了它在障碍散射、阿哈诺夫--玻姆哈密顿、扇形散射以及紧凑支撑势散射中的应用。

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From resolvent expansions at zero to long time wave expansions

We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundedness of the resolvent at high energy. We give applications to obstacle scattering, to Aharonov--Bohm Hamiltonians, to scattering in a sector, and to scattering by a compactly supported potential.

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arXiv - MATH - Spectral Theory

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