(2) Let S: E → e, s(aı, 02; ...) = (0, a1, a2, ...) be the forward shift operator. Show that the adjoint operator S* is the backward shift S*: (² → e, S*(a1, a2, . ..) = (a2, a3, ...). Verify that S*S = I, but SS* + I.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Hilbert spaces
(2) Let
S: & → E, S(a1, a2; .. .) = (0, a1, a2, ...)
be the forward shift operator. Show that the adjoint operator
S* is the backward shift
S*: ² → e, S*(a1,a2,.) =
(a2, a3, ...).
Verify that S*S = I, but SS* + I.
Transcribed Image Text:(2) Let S: & → E, S(a1, a2; .. .) = (0, a1, a2, ...) be the forward shift operator. Show that the adjoint operator S* is the backward shift S*: ² → e, S*(a1,a2,.) = (a2, a3, ...). Verify that S*S = I, but SS* + I.
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