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Convergence of the continuous wavelet transform with rotations in higher dimensions

  • Jaime NavarroEmail author
  • David Elizarraraz
Original Paper

Abstract

The continuous wavelet transform with rotations in higher dimensions is used to prove the regularity of distributions u under \(Qu = v\), where v is a distribution with compact support of class \(C^{\infty }(\mathbb {R}^n)\) in a neighborhood of some given point \(x = b_0\) in \(\mathbb {R}^n\) and where \(Q = \sum _{|\alpha | = p} c_{\alpha }\partial ^{\alpha }\) is a linear partial differential operator of order \(p > 0\) with constant coefficients \(c_{\alpha }\), under the assumption that the continuous wavelet transform with rotations converges in a neighborhood of \(x = b_0\).

Keywords

Admissible function Continuous wavelet transform with rotations Weak solution Regularity 

Mathematics Subject Classification

47A05 46N20 47N20 

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  1. 1.Departamento de ciencias basicasUniversidad Autonoma MatropolitanaMexico CityMexico

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