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Abstract: We prove global subelliptic estimates for systems of quadratic differentialoperators. Quadratic differential operators are operators defined in the Weylquantization by complex-valued quadratic symbols. In a previous work, wepointed out the existence of a particular linear subvector space in the phasespace intrinsically associated to their Weyl symbols, called singular space,which rules a number of fairly general properties of non-elliptic quadraticoperators. About the subelliptic properties of these operators, we establishedthat quadratic operators with zero singular spaces fulfill global subellipticestimates with a loss of derivatives depending on certain algebraic propertiesof the Hamilton maps associated to their Weyl symbols. The purpose of thepresent work is to prove similar global subelliptic estimates foroverdetermined systems of quadratic operators. We establish here a simplecriterion for the subellipticity of these systems giving an explicit measure ofthe loss of derivatives and highlighting the non-trivial interactions played bythe different operators composing those systems.



Author: Karel Pravda-Starov

Source: https://arxiv.org/



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