2 (25 points) Let n be a natural number and the real vector space Vn be defined by 1 Vn = span{ Cos x, sin x, cos 2x, si

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2 25 Points Let N Be A Natural Number And The Real Vector Space Vn Be Defined By 1 Vn Span Cos X Sin X Cos 2x Si 1 (202.23 KiB) Viewed 18 times

2 (25 points) Let n be a natural number and the real vector space Vn be defined by 1 Vn = span{ Cos x, sin x, cos 2x, sin 2x, ... , COS nr, sin nx}. COS X V2 Show that if şr(x) is the n-th partial sum of the Fourier series of a real square- for integrable function f(x), - < x < 77, then a - || Sn(x) – f(x)|| < ||Pn(2) – f(x)|| for all pn € Vng where ||g|| = VAS A \g(x) dx . TT -