# Discrete Fourier transform associated with generalized Schur polynomials

## TL;DR

This paper establishes a Plancherel formula for a broad family of discrete Fourier transforms linked to generalized Schur polynomials, unifying and extending classical sine and cosine transforms and their multivariate variants.

## Contribution

It introduces a unified framework for discrete Fourier transforms associated with generalized Schur polynomials, encompassing classical transforms and their multivariate generalizations.

## Key findings

- Proves the Plancherel formula for a four-parameter family of transforms
- Recovers classical DCT and DST transforms as special cases
- Extends to multivariate and symmetric generalizations

## Abstract

We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this recovers the sixteen classic discrete sine- and cosine transforms DST-1,...,DST-8 and DCT-1,...,DCT-8, as well as recently studied (anti-)symmetric multivariate generalizations thereof.