Prove that the most general solution to the functional equation (x) 2 (2x) is (x) (log 2 x) x where (z 1) (z) is any 1 periodic function ...

Lets start by making a substitution let y log2 x Then we can rewrite the functional ...

Prove that the most general solution to the functional equation (x) = 2 (2x) is (x) =

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Prove that the most general solution to the functional equation φ(x) = 2 φ(2x) is φ(x) = ƒ(log₂x)/x where ƒ(z + 1) = ƒ(z) is any 1 periodic function.

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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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Prove that the most general solution to the functional equation (x) = 2 (2x) is (x) =

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Applied Linear Algebra

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