ON CONVOLUTION TRANSFORMS WHOSE INVERSION FUNCTIONS HAVE COMPLEX ROOTS

Abstract

For convolution transforms it has been received inversion formula, when $\varphi(x) \in L^{2}(-\infty, +\infty)$, and inversion functions $E(x)=\prod\limits^{\infty}_{k=1}\Big(1- \dfrac{s^2}{a_k^2}\Big)$  have complex roots satisfying to conditions  $\sum\limits_{k=1}^{\infty}<+\infty, |\arg a_k|\leq\dfrac{π}{4}$.