Many of the operators one meets in several complex variables, such as the famous Lewy operator, are not locally solvable. Nevertheless, such an operator L can be thoroughly studied if one can find a suitable relative parametrix--an operator K such that LK is essentially the orthogonal projection onto the range of L. The analysis is by far most decisive if one is able to work in the real analytic, as opposed to the smooth, setting. With this motivation, the author develops an analytic calculus for the Heisenberg group. Features include: simple, explicit formulae for products and adjoints; simple representation-theoretic conditions, analogous to ellipticity, for finding parametrices in the calculus; invariance under analytic contact transformations; regularity with respect to non-isotropic Sobolev and Lipschitz spaces; and preservation of local analyticity. The calculus is suitable for doing analysis on real analytic strictly pseudoconvex CR manifolds. In this context, the main new application is a proof that the Szego projection preserves local analyticity, even in the three-dimensional setting.
Relative analytic parametrices are also constructed for the adjoint of the tangential Cauchy-Riemann operator. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
By:
Daryl Geller
Imprint: Princeton University Press
Country of Publication: United States
Dimensions:
Height: 254mm,
Width: 178mm,
Spine: 26mm
Weight: 851g
ISBN: 9780691608297
ISBN 10: 0691608296
Series: Princeton Legacy Library
Pages: 504
Publication Date: 14 July 2014
Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format: Paperback
Publisher's Status: Active
*FrontMatter, pg. i*CONTENTS, pg. vii*Introduction, pg. 3*1. Homogeneous Distributions, pg. 69*2. The Space Zqq,j, pg. 105*3. Homogeneous Partial Differential Equations, pg. 146*4. Homogeneous Partial Differential Operators on the Heisenberq Group, pg. 168*5. Homogeneous Singular Integral Operators on the Heisenberg Group, pg. 202*6. An Analytic Weyl Calculus, pg. 256*7. Analytic Pseudodifferent Operators on Hn: Basic Properties, pg. 285*8. Analytic Parametrices, pg. 376*9. Applying the Calculus, pg. 423*10. Analytic Pseudolocality of the Szego Projection and Local Solvability, pg. 453*References, pg. 489
