TL;DR
This paper investigates a family of closed operators with rank one perturbations defined by a specific holomorphic function, exploring their properties and potential applications in a simplified renormalization group model.
Contribution
It introduces a new class of operators with rank one perturbations characterized by a holomorphic family, relevant for toy models in renormalization group analysis.
Findings
Operators exhibit specific spectral properties.
Perturbation characterized by the function x^{m/2}.
Potential applications in simplified renormalization models.
Abstract
A holomorphic family of closed operators with a rank one perturbation given by the function is studied. The operators can be used in a toy model of renormalization group.
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