登入選單
返回Google圖書搜尋
The Fundamental Principle for Systems of Convolution Equations
Daniele Carlo Struppa
出版American Mathematical Soc., 1983
主題Mathematics / GeneralMathematics / Calculus
ISBN082182273X9780821822739
URLhttp://books.google.com.hk/books?id=ayPUCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋The fundamental principle of L. Ehrenpreis states that under suitable hypotheses, the solutions of a homogeneous constant coefficients PDE can be represented as finite sums of absolutely convergent integrals over certain varieties in C[superscript italic]n. In the present paper the author extends these results to the case of homogeneous [italic]N x [script]m systems of convolution equations. In the first part of the paper, he discusses and extends an interpolation formula developed by Berenstein and Taylor, and uses the generalized Koszul complex to solve the algebraic problems which arise when considering systems in more than one unknown: the main result is a fundamental principle for general systems of convolution equations, in spaces [italic]X as described above. The second part of the paper is devoted to the generalization of this (and a related) result to more general classes of spaces, e.g. to the LAU-spaces of Ehrenpreis.