Alberto Cialdea & Vladimir Maz’ya 
Semi-bounded Differential Operators, Contractive Semigroups and Beyond [PDF ebook] 

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
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2-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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