 # fa.purposeful evaluation – Decomposition of a duty into right-sided and left-sided duty Answer

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fa.purposeful evaluation – Decomposition of a duty into right-sided and left-sided duty

Here I outline a distribution $$fin D’$$ to breathe right-sided if supp $$fsubseteq [0,infty)$$ and defnote it by $$f_+$$ and if the supp $$fsubseteq (-infty,0]$$ it’s known as left-sided and denoted by $$f_-$$.

Now, it’s claimed that if $$f$$ is regionally integrable duty on $$mathbb{R}$$, then there’s a exclusive decomposition $$f=f_++f_-$$ the place $$f_+$$ is right-sided regionally integrable duty and $$f_-$$ is left sided regionally integrable duty.

For an instance:

If I’ve $$A(omega)=frac{1}{omega^2+9}$$
then I can discover a decomposition $$A_+(omega)=frac{i}{6(omega+3i)}$$ and $$A_-(omega)=frac{-i}{6(omega-3i)}$$ by inspection.

But, How do I discover such a decomposition for duty love
$$e^{-a x}theta(-x)$$ the place $$theta$$ is Heaviside step duty? Is there a common course of to search out such a decomposition?

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