Your browser does not support JavaScript!

Doctoral theses

Current Record: 34 of 34

Back to Results Previous page
Next page
Add to Basket
[Add to Basket]
Identifier uch.math.phd//1988katsoprinakis
Title Χαρακτηρισμός Δυναμοσειρών με μερικά αθροίσματα πάνω σε πεπερασμένο αριθμών κύκλων
Alternative Title Characterization of power series with partial sums lying on a finite number of circles
Creator Katsoprinakis, Emmanouel
Abstract Let K be the class of trigonometric series of power type, i.e. Taylor series Σ CZN for Z=EIX, whose partial sums for X in E, where E is a nondenumerable subset of (0,2π) lie on a finite number of circles (a priori depending on X) in the complex plane. The main result of this paper is that for every member of the class K, there exist a complex number Ω, /Ω/=1, and two positive integers N,K, such that for the coefficients cn we have: CM+Λ(Κ-Ν)=CΜΩΛ, Μ=Ν, Ν+1,...,Κ-1, Λ=1,2,3,... .thus, every member of the class K has (with minor modififications) a representation of the form: P(X)Σ ΕΙΚΝΧ, Ν=0 where P(X) is a suitable trigonometric polynomial and K a positive integer. The proof is elementary but rather long. This result is closely related to a theorem of Marcinkiewincz and Zygmund on the circular structure of the set of limit points of the sequence of partial sums of (C,1) summable Taylor series.
Issue date 1988-07-01
Date available 1997-06-6
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics--Doctoral theses
  Type of Work--Doctoral theses
Permanent Link https://elocus.lib.uoc.gr//dlib/f/3/1/metadata-dlib-1988katsoprinakis.tkl Bookmark and Share
Views 872

Digital Documents
No preview available

Download document
View document
Views : 17