Composition Operators on Paley-wiener Type Spaces: Role of Composition Operators on Various Signal Spaces

Sampling theory is an active field of research and it spans various fields from communication engineering to pure mathematics. Shannon's sampling theorems provide algorithms to reconstruct the bandlimited signals from their discrete sampling. In other words, these theories provide the crucial connection between continuous and discrete representations of information that enables one to store continuous signals as discrete, digital data with minimal error. In this book we have discussed extensively the theory of composition operators on various Hilbert spaces, especially reproducing kernel Hilbert spaces associated with positive definite kernels. The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited signals with spaces of entire functions of exponential type. Here we mainly focused on boundedness of composition and weighted composition operators on these spaces.