TY  - BOOK
AU  - Járai,Antal
ED  - SpringerLink (Online service)
TI  - Regularity Properties of Functional Equations in Several Variables
T2  - Advances in Mathematics
SN  - 9780387244143
U1  - 515.625 23
PY  - 2005///
CY  - Boston, MA
PB  - Springer US
KW  - MATHEMATICS
KW  - FUNCTIONAL EQUATIONS
KW  - DIFFERENCE AND FUNCTIONAL EQUATIONS
N1  - Preliminaries -- Steinhaus Type Theorems -- Boundedness and Continuity of Solutions -- Differentiability and Analyticity -- Regularity Theorems on Manifolds -- Regularity Results with Fewer Variables -- Applications
N2  - 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
UR  - http://dx.doi.org/10.1007/b105379
ER  -