# Spectral Analysis, Model Theory and Applications of Finite-Rank Perturbations

## TL;DR

This survey reviews spectral results related to finite-rank perturbations, emphasizing self-adjoint and unitary cases, with focus on singular perturbations and model representations.

## Contribution

It provides a comprehensive overview of classical and recent spectral results for finite-rank perturbations, highlighting singular cases and model representations.

## Key findings

- Summary of classical spectral results for finite-rank perturbations
- Discussion of recent advances in singular self-adjoint perturbations
- Analysis of model representations for unitary perturbations

## Abstract

This survey focuses on two main types of finite-rank perturbations: self-adjoint and unitary. We describe both classical and more recent spectral results. We pay special attention to singular self-adjoint perturbations and model representations of unitary perturbations.