Non-Elliptic Quadratic $\mathcal{PT}$-Symmetric Operators and Similarity to Self-Adjoint Operators

Stepan Malkov

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arXiv · 2608.28821

Non-Elliptic Quadratic $\mathcal{PT}$-Symmetric Operators and Similarity to Self-Adjoint Operators

Stepan Malkov

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Abstract

We prove a similarity result for non-self-adjoint non-elliptic quadratic $\mathcal{PT}$-symmetric operators with real spectrum satisfying a dynamical averaging condition. In particular, we show that such an operator is weakly similar to a self-adjoint operator precisely when the fundamental matrix of the associated quadratic form is diagonalizable.

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BibTeX RIS

Stepan Malkov. 2026-08-28. Non-Elliptic Quadratic $\mathcal{PT}$-Symmetric Operators and Similarity to Self-Adjoint Operators. https://arxiv.org/abs/2608.28821

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