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arXiv · 2510.11025

On singular points in the essential spectrum

Alexander Plakhotnikov
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Abstract

The paper investigates the existence of a limit in the operator norm for a family of operators $T_z(H)= F(H-z)^{-1}F^*$ for $z$ tending to the real axis. The conditions for the $H$ operator and the rigging operator $F$ are established, under which the limit exists. Special attention is paid to the separation of cases when the limit point belongs and does not belong to the point spectrum $H$.

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Alexander Plakhotnikov. 2025-10-13. On singular points in the essential spectrum. https://arxiv.org/abs/2510.11025

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