Home Competitions SCHWEITZER 1963 Problem 8
SCHWEITZER 1963 Problem 8
Let the Fourier series a 0 2 + ∑ k ≥ 1 ( a k cos k x + b k sin k x ) \frac{a_0}{2}+ \sum _{k\geq 1}(a_k\cos kx+b_k \sin kx) 2 a 0 + k ≥ 1 ∑ ( a k cos k x + b k sin k x ) f ( x ) f(x) f ( x ) a k 2 + b k 2 ≥ a k + 1 2 + b k + 1 2 ( k = 1 , 2 , . . . ) . a^2_k+b^2_k \geq a_{k+1}^2+b_{k+1}^2 \;(k=1,2,...)\ . a k 2 + b k 2 ≥ a k + 1 2 + b k + 1 2 ( k = 1 , 2 , ... ) . 1 h ∫ 0 2 π ( f ( x + h ) − f ( x − h ) ) 2 d x ( h > 0 ) \frac1h \int_0^{2\pi} (f(x+h)-f(x-h))^2dx \;(h>0) h 1 ∫ 0 2 π ( f ( x + h ) − f ( x − h ) ) 2 d x ( h > 0 ) h h h
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