# Properties of a vector operator

Suppose I have a vector operator which angle dependence is given by $$\hat O(\theta)=A\sin\theta+B\cos\theta+C$$ What can I say about $\hat O$? Sorry, I do realize that it is a bit vague. Assume $\hat O$ is an operator on the space of wavefunctions.

I can see that it is periodic with period $2\pi$, but what else?

Thank you.

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It is infinitely many times differentiable, satisfying a differential equation $y'+y'''=0$ and $y' = y^{(5)}$. – gt6989b Dec 11 '12 at 21:02