On the inversion of Bessel ultrahyperbolic kernel of Marcel Riesz (Q657121)

Summary: We define the Bessel ultrahyperbolic Marcel Riesz operator on the function \(f\) by \(U^{\alpha}(f) = R^B_{\alpha} \ast f\), where \(R^B_{\alpha}\) is Bessel ultrahyperbolic kernel of Marcel Riesz, \(\alpha \in \mathbb C\), the symbol \(\ast\) denotes the convolution, and \(f \in \mathcal S\), where \(\mathcal S\) is the Schwartz space of functions. Our purpose in this paper is to obtain the operator \(E^\alpha = (U^\alpha)^{-1}\) such that, if \(U^\alpha (f) = \varphi\), then \(E^\alpha \varphi = f\).