Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in L p ( R )

Jaime Navarro-Fuentes, Salvador Arellano-Balderas and Oscar Herrera-Alcántara
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Jaime Navarro-Fuentes: Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Mexico City 02200, Mexico
Salvador Arellano-Balderas: Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Mexico City 02200, Mexico
Oscar Herrera-Alcántara: Departamento de Sistemas, Universidad Autónoma Metropolitana, Mexico City 02200, Mexico

Mathematics, 2021, vol. 9, issue 5, 1-15

Abstract: The smoothness of functions f in the space L p ( R ) with 1 < p < ? is studied through the local convergence of the continuous wavelet transform of f . Additionally, we study the smoothness of functions in L p ( R ) by means of the local convergence of the semi-discrete wavelet transform.

Keywords: admissibility condition; the continuous wavelet transform; inversion formula; semi-discrete wavelet transform; tight frames (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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