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＜E-Book＞
Regularity Properties of Functional Equations in Several Variables / by Antal Járai
(Advances in Mathematics ; 8)

Edition	1st ed. 2005.
Publisher	(New York, NY : Springer US : Imprint: Springer)
Year	2005
Language	English
Size	IX, 363 p : online resource
Authors	*Járai, Antal author SpringerLink (Online service)
Subjects	LCSH:Difference equations LCSH:Functional equations FREE:Difference and Functional Equations
Notes	Preliminaries -- Steinhaus Type Theorems -- Boundedness and Continuity of Solutions -- Differentiability and Analyticity -- Regularity Theorems on Manifolds -- Regularity Results with Fewer Variables -- Applications 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 HTTP:URL=https://doi.org/10.1007/b105379

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