TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:2550000001333387 ID - ebk01:2550000001333387 ET - Course Book. LA - eng TI - Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability. (MN-37) PY - 1990 SN - 9781400860739 AU - Geller, Daryl, author. AB - 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 paperback editions preserve the original texts of these important books while presenting them in durable paperback 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. ER -Download RIS file
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001 | 9781400860739 | ||
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007 | cr |n||||||||n | ||
008 | 151027s1990||||||||||||o|||||||||||eng|| | ||
020 | a 9781400860739 | ||
024 | 7 | a 10.1515/9781400860739 2 doi | |
035 | a (DE-B1597)447664 | ||
035 | a (OCoLC)889253234 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
050 | 4 | a QA329.7 | |
050 | 4 | a QA329.7 b .G45 1990eb | |
072 | 7 | a MAT x 005000 2 bisacsh | |
072 | 7 | a MAT005000 2 bisacsh | |
082 | 4 | a 515/.7242 2 20 | |
082 | 4 | a 515/.7242 2 23 | |
100 | 1 | a Geller, Daryl, e author. | |
245 | 1 | 2 | a Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability. (MN-37) / c Daryl Geller. |
250 | a Course Book. | ||
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [1990] | |
264 | 4 | c Â©1990 | |
300 | a 1 online resource (504 pages) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Mathematical Notes ; v 37 | ||
505 | t Frontmatter -- t CONTENTS -- t Introduction -- t 1. Homogeneous Distributions -- t 2. The Space Z -- t 3. Homogeneous Partial Differential Equations -- t 4. Homogeneous Partial Differential Operators on the Heisenberq Group -- t 5. Homogeneous Singular Integral Operators on the Heisenberg Group -- t 6. An Analytic Weyl Calculus -- t 7. Analytic Pseudodifferent Operators on H -- t 8. Analytic Parametrices -- t 9. Applying the Calculus -- t 10. Analytic Pseudolocality of the Szego Projection and Local Solvability -- t References. | ||
520 | a 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 paperback editions preserve the original texts of these important books while presenting them in durable paperback 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. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 1990. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisherâ€™s Web site, viewed October 27 2015) | ||
650 | a Functions of several complex variables. | ||
650 | a MATHEMATICS v Calculus. | ||
650 | a MATHEMATICS x Mathematical Analysis. | ||
650 | a Pseudodifferential operators. | ||
650 | a Solvable groups. | ||
650 | 4 | a Functions of several complex variables. | |
650 | 4 | a Mathematics, other. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Mathematik. | |
650 | 4 | a Pseudodifferential operators. | |
650 | 4 | a Solvable groups. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Archive 1931-1999 z 978-3-11-044249-6 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Legacy Lib. eBook Package 1980-1999 z 978-3-11-041344-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Legacy Lib. eBook Package Science z 978-3-11-041359-5 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Mathematical Notes Backlist eBook Package z 978-3-11-049492-1 | |
830 | a Mathematical Notes. | ||
856 | 4 | u https://doi.org/10.1515/9781400860739 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400860739.jpg |
912 | a 978-3-11-041344-1 Princeton Legacy Lib. eBook Package 1980-1999 | ||
912 | a 978-3-11-041359-5 Princeton Legacy Lib. eBook Package Science | ||
912 | a 978-3-11-044249-6 Princeton eBook Package Archive 1931-1999 | ||
912 | a 978-3-11-049492-1 Princeton Mathematical Notes Backlist eBook Package | ||
912 | a GBV-deGruyter-alles | ||
912 | a GBV-deGruyter-PDA12STME | ||
912 | a GBV-deGruyter-PDA13ENGE | ||
912 | a GBV-deGruyter-PDA14ALL | ||
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912 | a GBV-deGruyter-PDA7ENG | ||
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