(a) Use duality to justify the formula f(x) '(x) f(0) '(,x) f '(0)8(x) when f C1 (b) Find a similar formula for f(x) (n) for the product of a sufficiently smooth function and the nth derivative of the delta function ...

(a) Use duality to justify the formula f(x)'(x) = f(0)'(,x) - f'(0)8(x) when f C1. (b)...

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(a) Use duality to justify the formula f(x)δ'(x) = f(0)δ'(,x) - f'(0)8(x) when f ∈ C1.
(b) Find a similar formula for f(x) δ (n) for the product of a sufficiently smooth function and the nth derivative of the delta function.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 18, 2016 09:04 AM

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(a) Use duality to justify the formula f(x)'(x) = f(0)'(,x) - f'(0)8(x) when f C1. (b)...

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