Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in <inline-formula><math display="inline"><mrow><msup><mi>L</mi><mi>p</mi></msup><mo>(</mo><mi mathvariant="double-struck">R</mi><mo>)</mo></mrow></math></inline-formula>

Abstract

The smoothness of functions f in the space Lp(R) with 1p∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(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