Academic Journal
THE FORMULA FOR THE SINGULARITY OF SZEGO KERNEL : I: The formula for the singularity of the Szegö kernel. I.
| Title: | THE FORMULA FOR THE SINGULARITY OF SZEGO KERNEL : I: The formula for the singularity of the Szegö kernel. I. |
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| Authors: | Kuranisha , Masatake |
| Source: | Asian J. Math. 8, no. 2 (2004), 353-362 |
| Publisher Information: | The Korean Mathematical Society, 2003. |
| Publication Year: | 2003 |
| Subject Terms: | Strongly pseudoconvex domains, singularity of Szegö kernel, Bergman kernel, singularity, 01 natural sciences, Pseudodifferential operators in several complex variables, generating function, conic neighbourhood, symplectic map, 0103 physical sciences, Integral representations, canonical kernels (Szegő, Bergman, etc.), Szegö kernel, ordinary differential equation of Hamilton type, strongly pseudoconvex hypersurface, 0101 mathematics |
| Description: | Let \(\Omega\) be a bounded domain in \(\mathbb C^n\) with smooth strongly pseudoconvex boundary \(\partial\Omega\). Fefferman found the formula for the Bergman kernel of \(\Omega\). Boutet de Monvel and Sjöstrand noted that the similar formula holds also for the Szegö kernel \(K^S\) near \(\partial\Omega\). The author develops a method of calculating explicitly the singularity of Szegö and Bergman kernel by using the process developed by Boutet de Monvel and Sjöstrand. To this end, the author writes down the equations which characterize the functions necessary in the construction, develops the method to solve these equations, and obtains explicitly the formula for the singularity at a critical point using the local data. In this calculation, the CR or the conformal geometric aspect of the formula for the singularity are ignored. |
| Document Type: | Article Other literature type |
| File Description: | application/xml; application/pdf |
| Language: | English |
| ISSN: | 0304-9914 |
| DOI: | 10.4134/jkms.2003.40.4.641 |
| DOI: | 10.4310/ajm.2004.v8.n2.a8 |
| Access URL: | http://society.kisti.re.kr/sv/SV_svpsbs03V.do?method=download&cn1=JAKO200311921888773 http://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2004/0008/0002/AJM-2004-0008-0002-a008.pdf https://zbmath.org/2066128 https://doi.org/10.4134/jkms.2003.40.4.641 https://zbmath.org/2148825 https://doi.org/10.4310/ajm.2004.v8.n2.a8 https://projecteuclid.org/euclid.ajm/1088090065 https://www.intlpress.com/site/pub/files/_fulltext/journals/ajm/2004/0008/0002/AJM-2004-0008-0002-a008.pdf https://projecteuclid.org/download/pdf_1/euclid.ajm/1088090065 https://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0008/0002/a008/index.php http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2003_v40n4_641 http://projecteuclid.org/euclid.ajm/1088090065 |
| Accession Number: | edsair.doi.dedup.....f8a73f2bbd3488831d647ac26b6bc9e5 |
| Database: | OpenAIRE |
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