6.(a)Let T : L²[0, 2π] → L²[0, 2ñ] be given by2πTf(x) =scos(xt) f(t) dt.Show that(i) T is self-adjoint.(ii) cos x and sin x are eigenvectors of T.

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Answered: 6. (a) Let T: L²[0, 2π] → L²[0, 2π] be…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = S cos(xt) f(t) dt. Show that (i) T is self-adjoint. (ii) cos x and sin x are eigenvectors of T.