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＜電子ブック＞
Regularity Properties of Functional Equations in Several Variables / by Antal Járai
(Advances in Mathematics ; 8)

版	1st ed. 2005.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	IX, 363 p : online resource
著者標目	*Járai, Antal author SpringerLink (Online service)
件　名	LCSH:Difference equations LCSH:Functional equations FREE:Difference and Functional Equations
一般注記	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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