Pandey-Upadhyay's wavelet transform and microlocal Sobolev singularities of functions
Akira Lee, Shinya Moritoh
TL;DR
This paper introduces a new approach to defining microlocal Sobolev singularities of functions using Pandey-Upadhyay's wavelet transform and compares it with H"ormander's classical microlocal singularities.
Contribution
It proposes a novel method for characterizing microlocal Sobolev singularities via wavelet transforms and analyzes its relation to existing H"ormander's framework.
Findings
Wavelet-based microlocal Sobolev singularities are effectively characterized.
Comparison shows similarities and differences with H"ormander's singularities.
The new approach offers potential advantages in analyzing function singularities.
Abstract
The aim of the paper is to define the microlocal Sobolev singularities of functions using Pandey-Upadhyay's wavelet transform and provide a comparison with H\"ormander's microlocal singularities.
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Taxonomy
TopicsImage and Signal Denoising Methods · Numerical methods in inverse problems · Mathematical Analysis and Transform Methods