Time-Frequency Analysis in the Unit Ball
Mathias Ionescu-Tira
TL;DR
This paper develops a time-frequency analysis framework for the complex unit ball using a windowed Helgason-Fourier transform, extending modulation and coorbit space theories to this setting.
Contribution
It introduces a windowed Helgason-Fourier transform and establishes atomic decompositions via Banach frames for the unit ball.
Findings
Established a new time-frequency analysis method for the unit ball.
Derived atomic decompositions using Banach frames.
Extended modulation and coorbit space theories to complex domains.
Abstract
As an appropriate analog of the Euclidean short-time Fourier transform, we study a windowed version of the Helgason-Fourier transform on the complex unit ball and translate the theory of modulation/coorbit spaces. As a result, atomic decompositions by means of Banach frames are obtained.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics · Numerical methods in inverse problems