Overview

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.

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9783319356709

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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)

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)

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