Regularity Properties of Functional Equations in Several Variables
This book is about regularity properties of functional equations. It c- tains, in a unified fashion, most of the modern results about regularity of non-composite functional equations with several variables. It also contains several applications including very recent ones. I hope that this book makes these results more accessible and easier to use for everyone working with functional equations. This book could not have been written without the stimulating at- sphere of the International Symposium on Functional Equations conference series and thus I am grateful to all colleagues working in this field. This series of conferences was created by JBnos Aczitl. I am especially grateful to him for inviting me to the University of Waterloo, Canada, which provided a peaceful working environment. I started this book in September 1998 during my stay in Waterloo. I thank Mikl6s Laczkovich, the referee of my C.Sc. dissertation very much for his remarks and suggestions. Between 1974 and 1997 I worked at Kossuth Lajos University, Debrecen, Hungary. Naturally, I am grateful to all members of the Debrecen School of functional equations. Finally, I would like to thank those of my colleagues, joint pieces of work with whom in one way or another are contained in this book: JAnos Aczkl, ZoltBn Darbczy, Roman Ger, Gyula Maksa, Zsolt PAles, Wolfgang Sander, and LAsz16 Szitkelyhidi. I thank my sons, Antal JArai Jr. and ZoltAn JBrai for correcting several errors of my "Hunglish"; all the remaining errors are mine.
Illustrates the basic ideas of regularity properties of functional equations by simple examples, then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashionContains several applications, including very recent ones