This paper proposes a new approach to the construction of wavelet decomposition, which is suitable for processing a wide range of information flows. The proposed approach is based on abstract functions with values in linear topological spaces. It is defined by embedded spaces and their projections. The proposed approach allows for adaptive ways of decomposition for the initial flow depending on the speed changes of the last one. The initial information flows can be real number flows, flows of complex and p-adic numbers, as well as flows of (finite or infinite) vectors, matrices, etc. The result is illustrated with examples of spline-wavelet decompositions of discrete flows, and also with the example of the decomposition of a continuous flow.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.