# Applications of an intersection formula to dual cones

## TL;DR

This paper presents a new proof of a duality theorem involving extremal quantities of trigonometric polynomials using an intersection formula on dual cones, with applications to integral estimates of positive definite functions.

## Contribution

It introduces a succinct proof of Révész's duality theorem utilizing an intersection formula on dual cones, offering new insights and applications in harmonic analysis.

## Key findings

- Provided a new proof of Révész's duality theorem
- Applied the intersection formula to integral estimates of positive definite functions
- Demonstrated the utility of dual cone intersection formulas in harmonic analysis

## Abstract

We give a succinct proof of a duality theorem obtained by R\'ev\'esz in 1991 which concerns extremal quantities related to trigonomertic polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show another application of this intersection formula which is related to the integral estimates of non-negative positive definite functions.