Regularity Properties of Functional Equations in Several Variables (Advances in Mathematics, 8) - Softcover

Jįrai, Antal

Softcover

ISBN 10: 1441937404 ISBN 13: 9781441937407

Publisher: Springer, 2010

Synopsis

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.

About this title

From the Back Cover:

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.

Review:

From the reviews of the first edition:

"This book is a welcome addition to the functional equations literature. ... The author does a masterful job of organizing and summarizing the results of the last 50 years and weaving them together into a coherent general theory. There are over 200 references. The book is very carefully written ... . The author has certainly achieved his stated goal of making these results ‘more accessible and easier to use for everyone working with functional equations.’" (Bruce Ebanks, Zentralblatt MATH, Vol. 1081, 2006)

About this edition

• Publisher: Springer
• Publication date: 2010
• ISBN 10: 1441937404
• ISBN 13: 9781441937407
• Binding: Paperback
• Number of pages: 372