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We have previously shown that a -fold holomorphic covering of a domain in the complex plane by another domain is extremal in the majorization principle for -valent functions and quadratic forms associated with Green's functions of these domains. In this paper, dual majorization principles involving both Green's and Neumann functions are obtained, in which -fold coverings are also extremal. The results are exemplified by applications of these principles to geometric function theory. [ABSTRACT FROM AUTHOR]

The paper deals with the asymptotics of solutions of the Volterra integral equation with difference kernel in the case where the free term has exponential growth. [ABSTRACT FROM AUTHOR]

The universality theoremasserts that the lower density of any set of shifts of the Riemann zeta-function which approximate a given analytic function with accuracy ɛ > 0 is strictly positive. It is proved that this set has strictly positive density for all but at most countably many ɛ > 0. [ABSTRACT FROM AUTHOR]