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عمومی::
تکیهگاه فشرده
It remains only to show that K = L2(F). But K is clearly dense in Cc(R), the
set of continuous functions on R with compact support, andCc(R) is dense in L2(F)
by Theorem 3.14 of Rudin (1987). This implies that the closure of K in L2(F) is
indeed L2(F). The mapping T defined on HX by (4.9) and (4.10) is thus a linear
inner-product preserving mapping of the closed linear spanHX = sp{Xt ,2 R} onto
L2(F).
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