Regularity Properties of Functional Equations in Several Variables: Advances in Mathematics, cartea 8
Autor Antal Járaien Limba Engleză Hardback – 3 mar 2005
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Specificații
ISBN-13: 9780387244136
ISBN-10: 0387244131
Pagini: 363
Ilustrații: IX, 363 p.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.7 kg
Ediția:2005
Editura: Springer Us
Colecția Springer
Seria Advances in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 0387244131
Pagini: 363
Ilustrații: IX, 363 p.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.7 kg
Ediția:2005
Editura: Springer Us
Colecția Springer
Seria Advances in Mathematics
Locul publicării:New York, NY, United States
Public țintă
ResearchCuprins
Preliminaries.- Steinhaus Type Theorems.- Boundedness and Continuity of Solutions.- Differentiability and Analyticity.- Regularity Theorems on Manifolds.- Regularity Results with Fewer Variables.- Applications.
Recenzii
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)
"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)
Textul de pe ultima copertă
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.
This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics.
Caracteristici
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