Items related to The Structure of Functions (Monographs in Mathematics)
Synopsis
This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier- strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m): m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N . One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . m E C. This resembles, at least formally, the Weier- strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces.
"synopsis" may belong to another edition of this title.
From the Back Cover
This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations.
The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.
- - -
The book under review can be regarded as a continuation of [his book on "Fractals and spectra", 1997] (...) There are many sections named: comments, preparations, motivations, discussions and so on. These parts of the book seem to be very interesting and valuable. They help the reader to deal with the main course.
(Mathematical Reviews)
About the Author
Hans Triebel was professor of mathematics at the Friedrich-Schiller-University Jena, Germany.
"About this title" may belong to another edition of this title.
- PublisherBirkhäuser
- Publication date2012
- ISBN 10 3034894945
- ISBN 13 9783034894944
- BindingPaperback
- LanguageEnglish
- Number of pages437
Buy New
View this item
US$ 99.70
US$ 20.92 shipping from United Kingdom to U.S.A.
Destination, rates & speedsOther Popular Editions of the Same Title
Search results for The Structure of Functions (Monographs in Mathematics)
Stock Image
The Structure of Functions
Seller: Chiron Media, Wallingford, United Kingdom
Seller rating 5 out of 5 stars
PF. Condition: New. Seller Inventory # 6666-IUK-9783034894944
Quantity: 10 available
Stock Image
The Structure of Functions (Monographs in Mathematics)
Seller: Lucky's Textbooks, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # ABLIING23Mar3113020038755
Quantity: Over 20 available
Stock Image
The Structure of Functions (Monographs in Mathematics)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9783034894944_new
Quantity: Over 20 available
Seller Image
The Structure of Functions
Published by
Springer, Basel, Birkhäuser Basel, Birkhäuser Nov 2012, 2012
ISBN 10: 3034894945
ISBN 13: 9783034894944
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m) : m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N~. One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . ~m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . ~m E C. This resembles, at least formally, the Weier strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces. 425 pp. Englisch. Seller Inventory # 9783034894944
Quantity: 2 available
Seller Image
The Structure of Functions
Published by
Birkhäuser Basel, Birkhäuser Basel, 2012
ISBN 10: 3034894945
ISBN 13: 9783034894944
New
Taschenbuch
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m) : m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N~. One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . ~m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . ~m E C. This resembles, at least formally, the Weier strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces. Seller Inventory # 9783034894944
Quantity: 1 available
Seller Image
The Structure of Functions
Print on DemandSeller: moluna, Greven, Germany
Seller rating 5 out of 5 stars
Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I Decompositions of Functions.- 1 Introduction, heuristics, and preliminaries.- 2 Spaces on ?n: the regular case.- 3 Spaces on ?n: the general case.- 4 An application: the Fubini property.- 5 Spaces on domains: localization and Hardy inequalities.- 6 Spaces. Seller Inventory # 4319309
Quantity: Over 20 available
Seller Image
The Structure of Functions
Published by
Birkhäuser Basel, Birkhäuser Basel Nov 2012, 2012
ISBN 10: 3034894945
ISBN 13: 9783034894944
New
Taschenbuch
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book deals with the symbiotic relationship between I Quarkonial decompositions of functions, on the one hand, and II Sharp inequalities and embeddings in function spaces, III Fractal elliptic operators, IV Regularity theory for some semi-linear equations, on the other hand. Accordingly, the book has four chapters. In Chapter I we present the Weier strassian approach to the theory of function spaces, which can be roughly described as follows. Let 'IjJ be a non-negative Coo function in]R. n with compact support such that {'ljJe - m) : m E zn} is a resolution of unity in ]R. n. Let 'IjJ!3(x) = x!3'IjJ(x) where x E ]R. n and {3 E N~. One may ask under which circumstances functions and distributions f in ]R. n admit expansions 00 (0. 1) f(x) = L L L ). . ~m'IjJ!3(2jx - m), x E ]R. n, n !3ENg j=O mEZ with the coefficients ). . ~m E C. This resembles, at least formally, the Weier strassian approach to holomorphic functions (in the complex plane), combined with the wavelet philosophy: translations x 1---4 x - m where m E zn and dyadic j dilations x 1---4 2 x where j E No in ]R. n. Such representations pave the way to constructive definitions offunction spaces.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 440 pp. Englisch. Seller Inventory # 9783034894944
Quantity: 1 available
Stock Image
The Structure of Functions
Seller: Revaluation Books, Exeter, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: Brand New. reprint edition. 440 pages. 10.00x7.01x1.00 inches. In Stock. Seller Inventory # x-3034894945
Quantity: 2 available