Cesaro limit of the Fourier transform

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                                      A.3 Decomposition of max{s, t}   133

However, the boundary condition x (0) 0 forces A B so that an eigenvec- tor must be a constant multiple of 1 x(t) cosh 2 t .

The direct computation of the right side of (A.5) with this function yields t 1 1 1 t cosh 2 s ds s cosh 2 s ds 0 1 1 t 1 1 2 sinh 2 cosh 2 cosh 2 t . (A.6)

Therefore, x(t) is an eigenvector if and only if 1 1 1 ...

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