We study regularization of ill-posed equations involving multiplication\noperators when the multiplier function is positive almost everywhere and zero\nis an accumulation point of the range of this function. Such equations\nnaturally arise from equations based on non-compact self-adjoint operators in\nHilbert space, after applying unitary transformations arising out of the\nspectral theorem. For classical regularization theory, when noisy observations\nare given and the noise is deterministic and bounded, then non…