# On extensions of commuting tuples of symmetric and isometric operators

## TL;DR

This paper investigates conditions for extending commuting tuples of symmetric and isometric operators to self-adjoint and unitary operators, proves a multidimensional Godi-Lucenko theorem, and applies it to a power-trigonometric moment problem.

## Contribution

It introduces new conditions for such extensions, establishes a multidimensional Godi-Lucenko theorem, and applies these results to solve a multidimensional moment problem.

## Key findings

- Conditions for extensions are identified.
- A multidimensional Godi-Lucenko theorem is proved.
- Application to a multidimensional power-trigonometric moment problem.

## Abstract

In this paper we study extensions of commuting tuples of symmetric and isometric operators to commuting tuples of self-adjoint and unitary operators. Some conditions which ensure the existence of such extensions are presented. A multidimensional analog of the Godi\v{c}-Lucenko Theorem is proved. An application to a multidimensional power-trigonometric moment problem is given.