IN THE PRESENT BOOK&NBSP;THE CONDITIONS ARE STUDIED FOR THE SEMI-BOUNDEDNESS OF PARTIAL DIFFERENTIAL OPERATORS WHICH IS INTERPRETED IN DIFFERENT WAYS. NOWADAYS ONE KNOWS RATHER MUCH ABOUT <I>L</I><SUP>2</SUP>-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 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)