О слабой сходимости квазибезгранично делимых распределений

We study a new class of so-called quasi-infinitely divisible laws which is a wide natural extension of the well-known class of infinitely divisible laws through the Levy–Khinchin representations. We are interested in criteria of weak convergence within this class. Under rather natural assumptions, we state assertions, which connect a weak convergence of quasi-infinitely divisible distribution functions with one special type of convergence of their Levy–Khinchin spectral functions. The latter convergence is not equivalent to the weak convergence. So we complement known results by Lindner, Pan, and Sato (2018) in this field.