Weighted pseudo \(\delta\)-almost automorphic functions and abstract dynamic equations (Q2021451)

The authors introduce the concept of matched spaces for time scales and use it to obtain the closedness of time scales under a nontranslational shift. This enables a group of irregular time scales to become regular, and even periodic. The authors have also introduced the concepts of \(\delta\)-almost automorphic and weighted \(\delta\)-almost automorphic functions under the matched spaces and presented certain important results. The collection of these results forms a new theory of almost automorphic functions for abstract dynamic equations. This new theory includes other dynamic equations on various quantum-like time scales.