About this book
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.
This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics.
Manifold differential equation equation function functional equation theorem variable
- DOI https://doi.org/10.1007/b105379
- Copyright Information Springer Science+Business Media, Inc. 2005
- Publisher Name Springer, Boston, MA
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-387-24413-6
- Online ISBN 978-0-387-24414-3
- About this book