Semi-bounded differential operators, contractive semigroups and beyond
By: Alberto Cialdea, Vladimir Maz'ya
Contributors: Mazʹi︠a︡, V. G.
Series: Operator theory, advances and applications -- v. 243; Operator theory, advances and applications -- v. 243.
Publisher: Birkhäuser/Springer
Published: 2014
Place of publication: Cham
Language: eng
Number of pages: 252
ISBN-13: 9783319045573; 9783319045580
Copyright date: 2014
Subjects: Differential operators; Operator theory
Description: This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L²-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, 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. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors' own contributions.--
Notes: Includes bibliographical references (p. 243-249) and index.
Table of contents: title: 1. Preliminary facts on semi-boundedness of forms and operators; title: 2. Lp-dissipativity of scalar second-order operators with complex coefficients; title: 3. Elasticity system; title: 4. Lp-dissipativity for systems of partial differential operators; title: 5. The angle of Lp-dissipativity; title: 6. Higher-order differential operators in Lp; title: 7. Weighted positivity and other related results.