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Balschke Products and Their Critical Values
KTH, School of Engineering Sciences (SCI).
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Blaschkeprodukter och deras kritiska värden (Swedish)
Abstract [en]

This paper concerns the problem of defining and computing a Blaschke product from a prescribed set of critical values. First a mathematical and theoretical background to Blaschke products and their critical values is presented, e.g. the Blaschke condition, important characteristics of finite Blaschke products and the uniqueness theorem. The problem is then presented and the paper walks through a computational method using gaussian curvature. In the same chapter the problem is then compared to some equivalent questions. Lastly two discrete methods are presented and compared. The first method uses the theory of circle packing as presented by Ken Stephenson and the second uses numerical methods to rewrite the problem as a quadratic matrix of linear equations.

Abstract [sv]

Den här rapporten handlar om problemet att bestämma och beräkna en Blaschkeprodukt från ett förutbestämt set av kritiska värden. Först presenteras en matematisk och teoretisk bakgrund till Balschkeprodukter, såsom Blaschkevillkoret, viktiga egenskaper hos ändliga Blaschke produkter och unikhetsteoremet. Problemet presenteras sedan och rapporten går igenom a beräkningsmetod som använder gaussisk kurvatur och teorin därbakom. Därefter, i samma kapitel, jämförs problemet med några ekvivalenta frågor. Avslutningsvis så presenteras två diskreta metoder för att lösa problemet. Den första använder teorin bakom cirkelpackning såsom det gjorde av Ken Stephenson och den andra använder numeriska metoder för att skriva om problemet till en kvadratisk matris av linjära ekvationer.

Place, publisher, year, edition, pages
2018. , p. 20
Series
TRITA-SCI-GRU ; 2018-107
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-230737OAI: oai:DiVA.org:kth-230737DiVA, id: diva2:1219078
Supervisors
Examiners
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-15Bibliographically approved

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