Polinomi i njihove derivacije

master's thesis

• Title (english): Polynomials and their derivatives
• Author: Anton Bogner
• Mentor: Sanja Varošanec (mentor)
• Mentor: Mea Bombardelli (sumentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Tomislav Bokulić (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Damir Pajić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom radu govorimo o poznatom teoremu, Bernsteinovoj nejednakosti za polinome i njihove derivacije. Polazeći od definicije polinoma i nekih bitnih teorema za holomorfne funkcije dolazimo do Bernsteinove nejednakosti i niza njezinih varijacija. Nadalje, proučavamo Erdos-Laxov i Turanov teorem za polinome, u kojima se pojavljuju uvjeti na položaj nultočaka. Na kraju dokazujemo nekoliko teorema u kojima se, za razliku od prijašnjih, javlja minimum modula polinoma i njegove prve derivacije.

Abstract (english)

In this paper we talk about the famous theorem, Bernstein’s inequality for polynomials and their derivatives. Starting from the definition of polynomials and some essential theorems for anayltic functions we obtain Bernstein’s inequality and a number of its variations. Furthermore, we study Erdos-Lax’s and Turan’s theorem for polynomials, which include conditions at the position of zeros. In the final chapter, we prove theorems in which, unlike the previous ones, the minimum of the modulus of the polynomial and its first derivation occurs.

• Keywords: Bernsteinova nejednakosti za polinome i njihove derivacije; teoremi za holomorfne funkcije; Erdos-Laxov teorem za polinome; Turanov teorem za polinome
• Keywords (english): Bernstein’s inequality for polynomials and their derivatives; Erdos-Lax’s theorem for polynomials; Turan’s theorem for polynomials
• Language: croatian
• URN:NBN: urn:nbn:hr:217:949290
• Study programme: Title: Mathematics and Physics Education; specializations in: Mathematics and Physics Education; Course: Mathematics and Physics Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: sveučilišni magistar edukacije matematike i fizike (sveučilišni magistar edukacije matematike i fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-01-30 11:00:43