Abstract
In Chapter 2 we obtained discrepancy estimates for the zero distribution of a polynomial p in connection with the equilibrium measure µ L of a Jordan curve or arc L. The basic quantities involved have been the two terms and where z 0 ∈ int L is fixed if L is a curve. In Section 2.3 we have outlined that it is possible to restrict the essential quantities to the outer bounds in the case of a Jordan arc. If L is a curve, we replace δ p,L by the smaller inner bound where L r − is the level line of the conformal mapping φ(z) of int L onto D normalized by φ(z 0) = 0, φ'(z 0) > 0, as in (1.4.5). Then the discrepancy estimates can be formulated in terms of e p,L (r) + δ p,L (r). In this chapter we shall discuss this approach carefully for general signed measures.
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.
