Prilog rešenju problema minimizacije Jensenovog funkcionala
Metapodaci
Prikaz svih podataka o disertacijiSažetak
Dissertation is written in 60 pages and is divided into next parts:
1. Preface (pages 2-7)
2. Introduction (pages 8-29)
3. Concentration polynomial in low degrees (pages 30-56)
4. References (pages 57-60) which is consisted of 52 items
Chapter 2 is divided into 9, and chapter 3 into 2 sections.
In preface a short historical review of polynomials and their importance and
position in mathematics are given. Especially interesting parts in preface are about number of zeros of polynomials in diferent sections of complex plane.
In section 2:1 there are well known characteristic of Mobijus' transformation
which will be used further in dissertation.
Section 2:2 of same chapter is consisted of relations of diferent norms which are
being introduced to vector spaces of all polynomials with complex coeficients.
In section 2:3 Hurwitz polynomials are explained. This class of polynomials
which was being examined at the end of 19th century has found its real position in
subject which is being examine...d in this dissertation.
Jensen's formula (which also appeared at the end of 19th century) is described
in section 4 from more aspects.
In sections 5, 6, 7 and 8 the relation among Jensen's formula, Hardy's spaces of
p degree, generalized Jensen's formula and Mahler's measure is given.
In section 9 in dissertation the story about lower and upper boundaries of
Jensen's functional is given (definition, motivation, some well known results and
some new results of the author).
The chapter 3 is consisted of results of the author which are related to lower
boundaries of Jensen's functional for polynomials which satisfy the condition (1:2) of dissertation. In that case extreme functions are being determined. the main purpose of author is making intervals [-2k;-2klog 2] whose ends presents asymptotically lower and upper boundary of best lower boundary of Jensen's functional determined. The part of those results is published in "Computers and Mathematics with Applications".