Semi-bounded Differential Operators, Contractive Semigroups and Beyond [Hardcover]

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.

This trail-blazing treatment of a new and emerging topic sets out the authors own research into differing interpretations of the semi-boundedness of partial differential operators. It examines function spaces that include the Hilbert and Banach varieties.

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 ilÃ