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Regularity Properties of Functional Equations in Several Variables (Advances in Mathematics, 8) - Hardcover
This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.
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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.
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This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics.
From the reviews of the first edition:
"This book is a welcome addition to the functional equations literature. ... The author does a masterful job of organizing and summarizing the results of the last 50 years and weaving them together into a coherent general theory. There are over 200 references. The book is very carefully written ... . The author has certainly achieved his stated goal of making these results ‘more accessible and easier to use for everyone working with functional equations.’" (Bruce Ebanks, Zentralblatt MATH, Vol. 1081, 2006)
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- PublisherSpringer
- Publication date2005
- ISBN 10 0387244131
- ISBN 13 9780387244136
- BindingHardcover
- Number of pages372
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Regularity Properties of Functional Equations in Several Variables (Advances in Mathematics (8)) by JĆ Ā”rai, Antal [Hardcover ]
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Regularity Properties of Functional Equations in Several Variables (Advances in Mathematics, 8)
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Book Description Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included. 376 pp. Englisch. Seller Inventory # 9780387244136
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Book Description Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 severa. Seller Inventory # 5909391
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Book Description Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. AudienceThis book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics. Seller Inventory # 9780387244136
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