Abstract
Some new properties of the multiplier are determined. A class of simply connected regions whose multiplier is a connected set is described. This class is characterized by the availability of spirals in a multiplier. Let the Gelfond — Leontiev generalized differentiation operator be continuous in the space of the analytic functions in simply connected region G of a complex plane. It is known to be presented as an operator of general complex convolution. The convolution kernel is generated by the many-valued function of one variable. The set M(G) with the property M(G)·G ⊆ G is called multiplier G. Let the region multiplier be connected, and it does not align with identity. It is proved in the paper that the functions under consideration will be univalent under these conditions. If multiplier G is unconnected, then there is always a generalized differentiation Gelfond—Leontiev operator with a many-valued generating function.
Highlights
Summary
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
