5
$\begingroup$

Consider an integral transform of Borel measures supported on $\mathbb{R}^n_+$ given by $$ f(z) =\int\limits_{\mathbb{R}^n_+} x^{z}\frac{\mu(dx)}{x} $$ where $z = (z_1,...,z_n) \in \mathbb{C}^n$, $x^z = x_1^{z_1}...x_n^{z_n}$ and $\frac{1}{x} = \frac{1}{x_1...x_n}$. This transform generalizes the classical Mellin transform. Is there some literature where I can read about it? Is there an inversion theorem for this case?

$\endgroup$
0
$\begingroup$

I found the following paper dealing with multidimensional Mellin inversion (it is not open access, though): https://iopscience.iop.org/article/10.1070/RM2007v062n05ABEH004459/pdf. It gives an inversion theorem for suitable classes of functions.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.