Details

Regularity Properties of Functional Equations in Several Variables

Advances in Mathematics, Band 8

von: Antal Járai
96,29 €
Verlag:	Springer
Format:	PDF
Veröffentl.:	30.03.2006
ISBN/EAN:	9780387244143
Sprache:	englisch
Anzahl Seiten:	363

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Als Gutschein

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

Inhaltsverzeichnis

Preliminaries.- Steinhaus Type Theorems.- Boundedness and Continuity of Solutions.- Differentiability and Analyticity.- Regularity Theorems on Manifolds.- Regularity Results with Fewer Variables.- Applications.

Back cover copy

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.

Sonderbeitrag

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 fashion Contains several applications, including very recent ones Includes supplementary material: sn.pub/extras