Just a draft !
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چکیده
Riemann approximately proved that every compact, connected Riemann surface is a projective algebraic curve, but the Dirichlet (minimum) principle he invoked was literally incorrect. The literal falsity amounts to the fact that a convex, closed subset of a Banach space need not have a unique element of least norm: it may have none, or infinitely-many. This minimum principle is true in a Hilbert space, as was observed, in effect, by Beppo Levi in 1906, who also created a Hilbert space to capture some aspect of the differentiability of functions, a forerunner of Sobolev spaces.
منابع مشابه
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تاریخ انتشار 2015