# Separability properties of singular degenerate abstract differential operators and applications

## TL;DR

This paper investigates the spectral and separability properties of singular degenerate elliptic operators in vector spaces, establishing conditions for their Fredholmness, spectral discreteness, and completeness of root elements.

## Contribution

It demonstrates that certain singular degenerate elliptic operators are separable and Fredholm, providing sharp resolvent estimates and spectral properties despite non-self-adjointness.

## Key findings

- Realization operator is separable and Fredholm in Lebesgue spaces.
- Spectrum of the operator is discrete.
- Root elements form a complete system.

## Abstract

In this paper, we study the separability and spectral properties of singular degenerate elliptic equations in vector valued spaces. We prove that a realization operator by this equation with some boundary conditions is separable and Fredholm in Lebesque spaces. The leading part of the associated differential operator is not self-adjoint. The sharpe estimate of the resolvent, discreetness of spectrum and completeness of root elements of this operator is obtained