SUBELLIPTIC ESTIMATES FOR OVERDETERMINED SYSTEMS OF QUADRATIC DIFFERENTIAL OPERATORS

Pravda-Starov, Karel

doi:https://doi.org/10.18910/23144

アクセス数:120件（2024-04-20 06:59 集計）

固定URL: https://doi.org/10.18910/23144

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タイトル	SUBELLIPTIC ESTIMATES FOR OVERDETERMINED SYSTEMS OF QUADRATIC DIFFERENTIAL OPERATORS
著者	著者名 Pravda-Starov, Karel
抄録	We prove global subelliptic estimates for systems of quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous work, we pointed out the existence of a particular linear subvector space in the phase space intrinsically associated to their Weyl symbols, called singular space, which rules a number of fairly general properties of non-elliptic quadratic operators. About the subelliptic properties of these operators, we established that quadratic operators with zero singular spaces fulfill global subelliptic estimates with a loss of derivatives depending on certain algebraic properties of the Hamilton maps associated to their Weyl symbols. The purpose of the present work is to prove similar global subelliptic estimates for overdetermined systems of quadratic operators. We establish here a simple criterion for the subellipticity of these systems giving an explicit measure of the loss of derivatives and highlighting the non-trivial interactions played by the different operators composing those systems.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	49(3)
ページ	563-611
刊行年月	2012-09
言語	英語
ハンドルURL	https://hdl.handle.net/11094/23144
DOI	https://doi.org/10.18910/23144
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 49, Number 3　(2012-9）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2012, 49(3), p. 563-611
DC.title	SUBELLIPTIC ESTIMATES FOR OVERDETERMINED SYSTEMS OF QUADRATIC DIFFERENTIAL OPERATORS
DC.creator	Pravda-Starov, Karel
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2012-09
DCTERMS.abstract	We prove global subelliptic estimates for systems of quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous work, we pointed out the existence of a particular linear subvector space in the phase space intrinsically associated to their Weyl symbols, called singular space, which rules a number of fairly general properties of non-elliptic quadratic operators. About the subelliptic properties of these operators, we established that quadratic operators with zero singular spaces fulfill global subelliptic estimates with a loss of derivatives depending on certain algebraic properties of the Hamilton maps associated to their Weyl symbols. The purpose of the present work is to prove similar global subelliptic estimates for overdetermined systems of quadratic operators. We establish here a simple criterion for the subellipticity of these systems giving an explicit measure of the loss of derivatives and highlighting the non-trivial interactions played by the different operators composing those systems.
DC.identifier	10.18910/23144
DC.format	application/pdf
citation_title	SUBELLIPTIC ESTIMATES FOR OVERDETERMINED SYSTEMS OF QUADRATIC DIFFERENTIAL OPERATORS
citation_author	Pravda-Starov, Karel
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2012-09
citation_journal_title	Osaka Journal of Mathematics
citation_volume	49
citation_issue	3
citation_firstpage	563
citation_lastpage	611
citation_public_url	https://hdl.handle.net/11094/23144
citation_doi_detail	10.18910/23144
citation_doi	https://doi.org/10.18910/23144

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