Historical Backround of wavelets and orthonormal systems: Recent results on positive linear operators reconstructed via wavelets

This survey paper provides a historical overview of wavelets and orthonormal systems, alongside recent findings related to linear positive operators reconstructed using wavelets. The first section delves into the historical and chronological development of wavelets, highlighting some of their significant properties. The second section examines linear positive operators constructed through wavelets, discussing their structural characteristics and approximation results. While the list included in this paper is comprehensive, it is not exhaustive. We apologize to any authors whose works on wavelets and wavelet-based operators are not cited in this paper.