The logarithmic conjugation theorem and conformal equivalence between multiply connected domains
(2022) In Bachelor’s Theses in Mathematical Sciences MATK11 20221Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
- Abstract
- The existence of a primitive of analytic functions, of an analytic logarithm
of zero-free analytic functions, and of a harmonic conjugate to any harmonic
function are fundamental propositions of elementary complex analysis, holding on simply-connected domains. We find that with suitable corrections,
analogous statements can be made on multiply connected domains, foremost
of these is these being the logarithmic conjugation theorem. This latter theorem is used to prove that isolated singularities on Hardy spaces are removable,
as well as to prove the doubly connected mapping theorem. For more general
multiply connected domains, we will prove conformal equivalence with slit
domains, in order to lay the foundation to the multipy... (More) - The existence of a primitive of analytic functions, of an analytic logarithm
of zero-free analytic functions, and of a harmonic conjugate to any harmonic
function are fundamental propositions of elementary complex analysis, holding on simply-connected domains. We find that with suitable corrections,
analogous statements can be made on multiply connected domains, foremost
of these is these being the logarithmic conjugation theorem. This latter theorem is used to prove that isolated singularities on Hardy spaces are removable,
as well as to prove the doubly connected mapping theorem. For more general
multiply connected domains, we will prove conformal equivalence with slit
domains, in order to lay the foundation to the multipy connected mapping
theorem. (Less) - Popular Abstract (Swedish)
- Vi behandlar i denna uppsats några generaliseringar av resultat i grundläggande komplex analys, såsom existens av logaritmiskt konjugat som generalisering av harmoniskt konjugat. Detta använder vi sedan bland annat för
att visa en sats om konforma avbildningar (d.v.s. avbildningar som bevarar
vinklar), som utgör en analogi med Riemanns avbildningssats för områden i
planet med ett hål. Detta resultat utgör sedan en bro till en ytterligare mer
generell sats, som behandlar sådana avbildningar mellan områden som har
n hål, och som kan visas med andra metoder.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9169131
- author
- Löfström, Martin LU
- supervisor
- organization
- alternative title
- Function theory in multiply connected domains
- course
- MATK11 20221
- year
- 2022
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor’s Theses in Mathematical Sciences
- report number
- LUNFMA-4136-2022
- ISSN
- 1654-6229
- other publication id
- 2022:K10
- language
- English
- id
- 9169131
- date added to LUP
- 2025-06-27 15:52:09
- date last changed
- 2025-06-27 15:52:09
@misc{9169131, abstract = {{The existence of a primitive of analytic functions, of an analytic logarithm of zero-free analytic functions, and of a harmonic conjugate to any harmonic function are fundamental propositions of elementary complex analysis, holding on simply-connected domains. We find that with suitable corrections, analogous statements can be made on multiply connected domains, foremost of these is these being the logarithmic conjugation theorem. This latter theorem is used to prove that isolated singularities on Hardy spaces are removable, as well as to prove the doubly connected mapping theorem. For more general multiply connected domains, we will prove conformal equivalence with slit domains, in order to lay the foundation to the multipy connected mapping theorem.}}, author = {{Löfström, Martin}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor’s Theses in Mathematical Sciences}}, title = {{The logarithmic conjugation theorem and conformal equivalence between multiply connected domains}}, year = {{2022}}, }