On large sieve inequalities involving pth powers of trigonometric polynomials

TL;DR

This paper develops new large sieve inequalities for sums involving pth powers of trigonometric polynomials, introducing a novel approach based on spectral radius and convolution operators rather than traditional L^2 techniques.

Contribution

It presents a new method for large sieve estimates that avoids L^2-techniques by analyzing convolution operators' norms and spectral radii.

Findings

Extended large sieve inequalities for pth powers of trigonometric polynomials

Introduced a spectral radius-based approach to sieve estimates

Provided bounds independent of traditional L^2 methods

Abstract

In this paper, we extend the large sieve type estimates to sums involving pth powers of trigonometric polynomials. An approach to such estimates that does not rely on the usual L^2-technique is given. Our method is based on comparing the norm and the spectral radius of convolution operators on a normed space of trigonometric polynomials.