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Mathematics - Dynamical Systems & Differential Equations | Regularity Properties of Functional Equations in Several Variables

Regularity Properties of Functional Equations in Several Variables

Series: Advances in Mathematics, Vol. 8

Járai, Antal

2005, IX, 363 p.

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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.

Content Level » Research

Keywords » Manifold - differential equation - equation - function - functional equation - theorem - variable

Related subjects » Dynamical Systems & Differential Equations

Table of contents / Sample pages 

Preliminaries.- Steinhaus Type Theorems.- Boundedness and Continuity of Solutions.- Differentiability and Analyticity.- Regularity Theorems on Manifolds.- Regularity Results with Fewer Variables.- Applications.

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