The Module Structure of lim
نویسنده
چکیده
This paper shows that the projective and inductive limits, lim ←Ð Hs and lim Ð→ Hs, of the Sobolev spaces are flat modules over the ring C[∂1, . . . , ∂n] of constant coefficient differential operators. This can be interpreted as a GAGA type result for the affine space Rn, and as a response to a remark of V.I.Danilov [in Algebraic Geometry II: Cohomology of Algebraic Varieties, Encyclopaedia of Mathematical Sciences, 1995]. Such results also appear in the theory of control of dynamical systems.
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تاریخ انتشار 2009