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∫ e^{z*(z - z0)}f(z) dz*dz

is proportional tof(zmuch in the same way that_{0})

(1/2π)∫ e^{iy(x - x0)}f(x) dxdy

= ∫ δ(x - x_{0})f(x) dx

= f(x_{0})

Is this true? Could someone help convince me of it, or point me to a text?

I would say that even if true, it would beincorrectto say that

∫ e^{z*(z - z0)}dz* = δ(z - z_{0})

because the integration over dz and dz* cannot be done independently in the same way that a surface integral over dxdy in the plane can (sometimes) be separated into independent integrations over x and y. Or can it?

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# Dirac delta function on the complex plane?

Can you offer guidance or do you also need help?

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