A Characterisation of the Euclidean Fourier transform on the Schwartz space

2016/04/19 by R‎. ‎Lakshmi Lavanya, Lavanya, R. Lakshmi
Mathematics · #42A38 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1604.05551

openalex publication_date 2016/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a characterisation of the Fourier transform on the space of Schwartz class functions on ℝⁿ. The result states that any appropriately additive bijection of the Schwartz space onto itself, which interchanges convolution and pointwise products is essentially the Fourier transform.

Related

• A Novel Schwartz Space for the (k,(2)/(n))-Generalized Fourier Transform
• A Characterisation of the Fourier transform on the Schwartz-Bruhat space of locally compact Abelian groups
• On the Fourier transform of Schwartz functions on Riemannian Symmetric Spaces
• Mapping properties of Fourier transforms, II
• A characterization of Fourier transforms