Regularity Properties of Functional Equations in Several Variables
By: Járai, Antal [author.].
Contributor(s): SpringerLink (Online service).
Material type:
BookSeries: Advances in Mathematics: 8Publisher: Boston, MA : Springer US, 2005.Description: IX, 363 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387244143.Subject(s): Mathematics | Difference equations | Functional equations | Mathematics | Difference and Functional EquationsDDC classification: 515.625 | 515.75 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK6237 |
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.
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