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SPIRES-BOOKS: FIND KEYWORD FUNCTIONS OF REAL VARIABLES *END*INIT* use /tmp/qspiwww.webspi1/8403.22 QRY 131.225.70.96 . find keyword functions of real variables ( in books using www

 Call number: SPRINGER-2011-9781441998132:ONLINE Show nearby items on shelf Title: Nonelliptic Partial Differential Equations [electronic resource] : Analytic Hypoellipticity and the Courage to Localize High Powers of T Author(s): David S Tartakoff Date: 2011 Publisher: New York, NY : Springer New York Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book fills a real gap in the analytical literature. After many years and many results of analytic regularity for partial differential equations, the only access to the technique known as $(T^p)_\phi$ has remained embedded inthe research papers t hemselves, making it difficult for a graduate student or a mature mathematician in another discipline to master the technique and use it to advantage. This monograph takes a particularly non-specialist approach,one might even say gentle, to smoothly bring the reader into the heart of the technique and its power, and ultimately to show many of the results it has been instrumental in proving. Another technique developed simultaneously by F.Treves is developed and compared and contrasted to ours. The techni ques developed here are tailored to proving real analytic regularity to solutions of sums of squares of vector fields with symplectic characteristic variety andothers, real and complex. The motivation came from the field of several complex variables and t he seminal work of J. J. Kohn. It has found application in non-degenerate (strictly pseudo-convex) and degenerate situations alike, linearand non-linear, partial and pseudo-differential equations, real and complex analysis. The technique is utterly elemen tary, involving powers of vector fields and carefully chosen localizing functions. No knowledge of advancedtechniques, such as the FBI transform or the theory of hyperfunctions is required. In fact analyticity is proved using only $C^\infty$ techniques. The book is intended for mathematicians from graduate students up, whether inanalysis or not, who are curious which non-elliptic partial differential operators have the property that all solutions must be real analytic. Enough background is provided to pr epare the reader with it for a clear understanding of thetext, although this is not, and does not need to be, very extensive. In fact, it is very nearly true that if the reader is willing to accept Note: Springer eBooks Contents: 1. What this book is and is not 2. Brief Introduction 3.Overview of Proofs 4. Full Proof for the Heisenberg Group 5. Coefficients 6. Pseudo differential Problems 7. Sums of Squares and Real Vector Fields 8. \bar{\partial} Neumann and the Boundary Laplacian 9. Symmetric Degeneracies 10. Details of the Previous Chapter 11. Non symplectic Strategem ahe 12.Operators of Kohn Type Which Lose Derivatives 13. Non linear Problems 14. Treves' Approach 15. Appendix Bibliography ISBN: 9781441998132 Series: e-books Series: SpringerLink (Online service) Series: Developments in Mathematics, 1389-2177 : v22 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis (Mathematics) , Differential equations, partial Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE

 Call number: SPRINGER-2010-9788847017849:ONLINE Show nearby items on shelf Title: Mathematical Analysis II [electronic resource] Author(s): Claudio Canuto Anita Tabacco Date: 2010 Publisher: Milano : Springer Milan Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical secondlecture course in Calcu lus as offered in most Italian universities. While the subject matter known as Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on Calculus 2'can varya lot, resulting in a bigger flexibility. Fo r these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is notcomparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book.On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested read er may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. TheAuthors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the studentput his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined Note: Springer eBooks ISBN: 9788847017849 Series: e-books Series: SpringerLink (Online service) Series: Universitext Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential Equations , Differential equations, partial Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE