# Convergence of lacunary SU(1,1)-valued trigonometric products

## TL;DR

This paper investigates the convergence properties of lacunary SU(1,1)-valued trigonometric products, providing new insights into their $L^p$-convergence and almost everywhere convergence as nonlinear analogues of classical series results.

## Contribution

It characterizes the convergence of lacunary SU(1,1)-valued trigonometric products in $L^p$-metric and almost everywhere, extending classical results to a nonlinear matrix-valued setting.

## Key findings

- Characterization of $L^p$-convergence for lacunary SU(1,1) products
- Conditions for almost everywhere convergence of these products
- Extension of classical lacunary series results to matrix groups

## Abstract

This note attempts to study lacunary trigonometric products with values in the matrix group SU(1,1) in analogy with lacunary trigonometric series. The central questions are the characterization of their convergence in an appropriately define $L^p$-metric and the characterization of their convergence almost everywhere. These can be interpreted as nonlinear analogues of the classical results by Zygmund and Kolmogorov.