Semi-bounded differential operators, contractive semigroups and beyond
Author(s)
Bibliographic Information
Semi-bounded differential operators, contractive semigroups and beyond
（Operator theory : advances and applications, v. 243）
Birkhäuser , Springer, c2014
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 243-249) and index
Description and Table of Contents
Description
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.
Table of Contents
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.
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