The discussion revolves around verifying the sifting property of the inverse Mellin transformation of the Dirac delta function, specifically the expression ##\frac{1}{2\pi i} \int_{-i\infty}^{i\infty} e^{-sa}e^{st} ds##. Participants are exploring the implications of this transformation in relation to the sifting property, which states that ##\int_{-\infty}^{\infty} f(t) \delta(t-a) dt = f(a)##.
The discussion is ongoing, with participants expressing confusion about the steps needed to verify the sifting property. Some have proposed methods to replace the delta function with the Mellin transform but are struggling to reconcile their results with the expected outcome of obtaining ##f(a)##. There is no explicit consensus yet, but several participants are actively engaging with the problem and offering guidance.
Participants note discrepancies between their findings and textbook definitions, particularly regarding the limits of integration and the behavior of the Mellin transform at specific points. There is a shared uncertainty about how to properly apply the sifting property in this context.
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.