Uniqueness theorem for representation of functions by multiplicative transformations (Q1803066)

The paper deals with the integral transform \(\int^ \infty_ 0 a(x) \chi(x,y) dx\) with \(a(x) \in L^ 1_{\text{loc}} [0,\infty)\), where the kernel \(\chi(x,y)\) is a continual analogue of multiplicative orthonormal systems. An inversion formula of this transform is found by means of summability of \((C,1)\) type.