This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.
Publisher: Birkhauser Verlag AG
Number of pages: 306
Weight: 538 g
Dimensions: 235 x 165 x 18 mm
Edition: 2010 ed.
From the reviews:
"The authors present a nice unified approach for deriving pseudo-differential calculus on Rd and interesting recent results for classes of pseudo-differential operators defined globally on Rd. ... The book is well written; an extended summary is given at the beginning of every chapter while at the end the authors provide comments and remarks that illustrate the historical background, previous contributions and references in the field. This book looks very interesting for researchers and Ph.D. students studying, broadly speaking, PDEs and pseudo-differential operators globally in Rd." (Todor V. Gramchev, Mathematical Reviews, Issue 2011 k)
"Describes in a clear way the basic theory as well as new trends and results in global pseudo-differential operators calculus ... . well written and organized at a difficulty level that precisely meets the target audience's needs. Mathematics students as well as researchers in mathematical analysis will find this book an excellent resource to introduction into the field of pseudo-differential operator calculus. ... serve as a textbook for graduate-level courses in pseudo-differential operators. ... may also be useful and interesting for experienced PDEs researchers." (Andrzej Myslinski, Control and Cybernetics, Vol. 39 (4), 2010)
"The subject of the book are pseudo-differential operators on Euclidean spaces. ... The book is structured as follows. After a well-written introduction which summarizes the main ingredients of the book, the book starts with Chapter 0, which summarizes the relevant background. The main content is then structured in six chapters, each of which starts with a summary. This contributes to making the book accessible and pleasant to read." (Bernd Ammann, Zentralblatt MATH, Vol. 1257, 2013)
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