Nonelliptic Partial Differential Equations:Analytic Hypoellipticity and the Courage to Localize High Powers of T (Developments in Mathematics, 22)

by: David S. Tartakoff (Author)

Publisher: Springer
Edition:2011th

Publication Date: July 26, 2011

Language: English

Print Length: 211 pages

ISBN-10: 1441998128

ISBN-13: 9781441998125

Book Description

This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this technique and its power and flexibility.
This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this technique and its power and flexibility.

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