Regularity Properties of Functional Equations in Several Variables

This book is about regularity properties of functional equations. In the second part of his fifth problem, Hilbert asked, concerning functional equations, "In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumption? This book contains, in a unified fashion, most of the modern results about regularity of non-composite functional equations with several variables. These results show that "weak regularity properties, say measurability or continuity, of solutions imply that they are in C[infinity], and hence the equation can be reduced to a differential equation. A long introduction highlights the basic ideas for beginners. Several applications are also included. §Audience§This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics.This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.