Executive Summary : | The study aims to analyze the error in sampling theory associated with discrete wavelets. It will focus on obtaining the sampling and reconstruction formula for Multiplication Invariant spaces in a sigma finite measure space X with H-valued functions/signals/images. The sampling formula will be connected to the Shift invariant subspace V, the core space of wavelets. Wavelet/shearlets have a growing impact on many fields due to their unifying role in theory and application success. The main aim is to study the Minimum Error Sampling and Approximation Error, choosing a specific window as a spline in the core space. The development of this theory will contribute significantly to recent developments in sampling theory and its connection with wavelet analysis. The study is important as it allows for the theory of sampling over group settings and facilitates connections with quantum physics. |