A scalar valued Fourier transform for the Heisenberg group
Sundaram Thangavelu
TL;DR
This paper introduces a scalar valued Fourier transform for the Heisenberg group, establishing fundamental properties and connecting it with existing Fourier analysis theorems.
Contribution
It proposes a new scalar Fourier transform for the Heisenberg group, called the Strichartz Fourier transform, with foundational properties and reinterpretations of classical theorems.
Findings
Defined the scalar Fourier transform for the Heisenberg group
Proved inversion, Plancherel, and Riemann-Lebesgue properties
Reformulated classical theorems using the new transform
Abstract
We define a scalar valued Fourier transform for functions on the Heisenberg group and establish some of its basic properties like inversion formula, Plancherel theorem and Riemann-Lebesgue lemma. We also restate certain well known theorems for the group Fourier transform in terms of the new transform which we would like to call Strichartz Fourier transform.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Algebraic and Geometric Analysis · advanced mathematical theories