An error estimation of absolutely continuous signals and solution of Abel’s integral equation using the first kind pseudo-Chebyshev wavelet technique

Abstract

This paper introduces a novel computational strategy for addressing challenges in approximation theory. It focuses on the use of first-kind pseudo-Chebyshev wavelet approximations and the methodology and evaluation of the error for a specific function are outlined, along with practical instances to showcase the method’s effectiveness and efficiency. This approach is motivated by the need for highly efficient and precise methods for function representation and the error reduction in this domain. The paper also establishes the error of a function associated with the class of absolutely continuous functions using first-kind pseudo-Chebyshev wavelets via orthogonal projection operators, highlighting their precision and theoretical optimality within the domain of wavelet analysis. Additionally, the use of wavelet approximation to solve Abel’s integral equation is demonstrated by computing the approximate solution using first kind pseudo-Chebyshev wavelet.

Keywords

• Absolute continuity
• Wavelets
• Multiresolution analysis
• Pseudo-Chebyshev functions
• First kind pseudo-Chebyshev wavelets
• Pseudo-Chebyshev wavelet coefficient