The discussion focuses on verifying the sifting property of the inverse Mellin transformation of the Dirac delta function, specifically the integral ##\frac{1}{2\pi i} \int_{-i\infty}^{i\infty} e^{-sa}e^{st} ds##. Participants analyze the relationship between this integral and the property ##\int_{-\infty}^{\infty} f(t) \delta(t-a) dt = f(a)##, expressing confusion over the presence of the ##\frac{1}{2\pi}## factor and the implications of integrating with respect to ##t##. The conversation emphasizes the need to demonstrate that the Mellin transform behaves like the delta function, ultimately leading to the conclusion that further clarification on the integration process is necessary.
PREREQUISITESMathematicians, physicists, and engineers working with signal processing, integral transforms, and complex analysis who need to understand the sifting property of the Dirac delta function in the context of Mellin transformations.
Exactly what are you supposed to verify?EpselonZero said:Since I have to verify that, I don't think I can use that right away. I see what you meant now.
However, if this is the thing I have to show it makes no sense to use it.
I wouldn't say that I'm using the result I'm trying to show.EpselonZero said:Since I have to verify that, I don't think I can use that right away. I see what you meant now.
However, if this is the thing I have to show it makes no sense to use it.