Semi-bounded Differential Operators, Contractive Semigroups and Beyond
Springer International Publishing (Verlag)
978-3-319-35670-9 (ISBN)
In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L2-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.
Introduction.- 1 Preliminary facts on semi-boundedness of forms and operators.- 2 Lp-dissipativity of scalar second order operators with complex coefficients.- 3 Elasticity system.- 4 Lp-dissipativity for systems of partial differential operators.- 5 The angle of Lp-dissipativity.- 6 Higher order differential operators in Lp.- 7 Weighted positivity and other related results.- References.
"This book is valuable; it contains a lot of new information and deep, complicated proofs. ... it is a very good book, and every serious research university library should get it. I expect it to inspire new research." (Jerome A. Goldstein, Bulletin of the American Mathematical Society, Vol. 55 (1), January, 2018)
"The book is logically ordered and clearly written ... . It will be of interest to specialists and graduate students working on partial differential operators in function spaces." (Hector O. Fattorini, zbMATH 1317.47002, 2015)
| Erscheinungsdatum | 29.08.2016 |
|---|---|
| Reihe/Serie | Operator Theory: Advances and Applications |
| Zusatzinfo | XIII, 252 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Differential calculus and equations • elasticity system • Functional analysis and transforms • L^p-dissipativity • mathematics and statistics • operator theory • Partial differential equations • partial differential operators • semi-boundedness • weighted positivity |
| ISBN-10 | 3-319-35670-4 / 3319356704 |
| ISBN-13 | 978-3-319-35670-9 / 9783319356709 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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