"블라쉬케 곱 (Blaschke product)"의 두 판 사이의 차이

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==개요==
  
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*  다음과 같은 꼴의 뫼비우스 변환들은 단위원을 단위원으로 보내는 전단사 해석함수이다:<math>B(a,z)=\frac{|a|}{a}\frac{z-a}{1-\bar{a}z}</math>
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*  Blaschke product는 이러한 꼴의 함수들의 유한 또는 무한곱으로 쓰여짐.:<math>B(z)=\prod_n B(a_n,z)</math>
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* 단위원에서 정의된 함수로 주어진 점에서 zero 를 갖는 해석함수를 만들기 위해 사용됨
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==타원과 3차 블라쉬케 곱==
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*  다음과 같은 3차의 블라쉬케 곱을 생각하자:<math>B(z)=z\frac{z-a}{1-\bar{a}z}\frac{z-b}{1-\bar{b}z}</math>
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*  단위원 위의 점 <math>\lambda</math> 에 대하여, <math>B(z)=\lambda</math> 의 세 해를 <math>z_ 1,z_ 2,z_ 3</math> 로 두면, 세 직선 <math>\overline{z_ 1z_ 2},\overline{z_ 2 z_ 3},\overline{z_ 1 z_ 3}</math> 은 다음 타원에 접한다:<math>|w-a|+|w-b|=|1-\bar{a}b|</math>
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* <math>a=0.5,b=-0.4+0.4 i</math> 로 두고, 다양한 <math>\lambda</math> 에 대하여 위의 결과를 적용하여 얻은 그림
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[[파일:블라쉬케 곱(Blaschke product)1.gif]]
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* '''[DPR2002]''' 참조
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==역사==
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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* [[수학사 연표]]
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==메모==
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* [http://www.jstor.org/stable/10.2307/3072367 ]http://www.jstor.org/stable/10.2307/3072367
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* http://math.stackexchange.com/questions/104806/question-regarding-infinite-blaschke-product
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* Math Overflow http://mathoverflow.net/search?q=
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==관련된 항목들==
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==매스매티카 파일 및 계산 리소스==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxMWtGaTRianZfVUE/edit
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==수학용어번역==
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*  단어사전
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** http://translate.google.com/#en|ko|
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** http://ko.wiktionary.org/wiki/
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* 발음사전 http://www.forvo.com/search/
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==사전 형태의 자료==
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* http://ko.wikipedia.org/wiki/
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* http://en.wikipedia.org/wiki/Blaschke_product
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* [http://www.encyclopediaofmath.org/index.php/Main_Page Encyclopaedia of Mathematics]
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* [http://dlmf.nist.gov NIST Digital Library of Mathematical Functions]
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* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations]
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==리뷰논문, 에세이, 강의노트==
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* Garcia, Stephan Ramon, Javad Mashreghi, and William T. Ross. “Finite Blaschke Products: A Survey.” arXiv:1512.05444 [math], December 16, 2015. http://arxiv.org/abs/1512.05444.
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==관련논문==
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* Fletcher, Alastair. “Blaschke Products and Domains of Ellipticity.” arXiv:1408.2418 [math], August 11, 2014. http://arxiv.org/abs/1408.2418.
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* '''[DPR2002]'''Daepp, Ulrich, Pamela Gorkin, and Raymond Mortini. 2002. Ellipses and Finite Blaschke Products. <em>The American Mathematical Monthly</em> 109 (9) (November 1): 785-795. doi:[http://dx.doi.org/10.2307/3072367 10.2307/3072367].
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== 노트 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q4380191 Q4380191]
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===말뭉치===
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# Thus, Blaschke's theorem describes the sequences of zeros of all possible Blaschke products.<ref name="ref_9e2883be">[https://encyclopediaofmath.org/wiki/Blaschke_product Encyclopedia of Mathematics]</ref>
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# P.M. Tamrazov, "Conformal-metric theory of doubly connected domains and the generalized Blaschke product" Soviet Math.<ref name="ref_9e2883be" />
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# We present four algorithms to determine whether or not a Blaschke product is a composition of two non-trivial Blaschke products and, if it is, the algorithms suggest what the composition must be.<ref name="ref_41869d8e">[https://www.sciencedirect.com/science/article/pii/S0022247X1500058X Decomposing finite Blaschke products]</ref>
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# The final algorithm looks at inverse images under the Blaschke product.<ref name="ref_41869d8e" />
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# Blaschke products were introduced by Wilhelm Blaschke (1915).<ref name="ref_17324500">[https://en.wikipedia.org/wiki/Blaschke_product Blaschke product]</ref>
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# This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields.<ref name="ref_4043241e">[https://www.springer.com/gp/book/9783319782461 Finite Blaschke Products and Their Connections]</ref>
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# Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products.<ref name="ref_4043241e" />
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# This book gathers the principal results about Blaschke products heretofore scattered in research papers over the past 70 years and provides an extensive bibliography of over 300 items.<ref name="ref_c68c4e61">[https://www.press.umich.edu/9690151/blaschke_products Blaschke Products]</ref>
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# It is hoped that research workers in and students of function theory will find the book a useful guide and reference to the subject of Blaschke products.<ref name="ref_c68c4e61" />
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# All examples of Blaschke products constructed so far to prove this result have their zeros located on a ray.<ref name="ref_8bd64d4e">[https://projecteuclid.org/euclid.ijm/1258136177 Girela , Peláez : On the derivative of infinite Blaschke products]</ref>
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# A Blaschke product always belongs to the set I of inner functions; it has norm 1 and radial limits of modulus 1 almost everywhere.<ref name="ref_dd2495ff">[https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/some-lemmas-on-interpolating-blaschke-products-and-a-correction/B6435C2F5CC73570416AB722733D092D Some Lemmas on Interpolating Blaschke Products and a Correction]</ref>
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===소스===
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<references />
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[[분류:복소함수론]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q4380191 Q4380191]
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===Spacy 패턴 목록===
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* [{'LOWER': 'blaschke'}, {'LEMMA': 'product'}]

2021년 2월 17일 (수) 04:46 기준 최신판

개요

  • 다음과 같은 꼴의 뫼비우스 변환들은 단위원을 단위원으로 보내는 전단사 해석함수이다\[B(a,z)=\frac{|a|}{a}\frac{z-a}{1-\bar{a}z}\]
  • Blaschke product는 이러한 꼴의 함수들의 유한 또는 무한곱으로 쓰여짐.\[B(z)=\prod_n B(a_n,z)\]
  • 단위원에서 정의된 함수로 주어진 점에서 zero 를 갖는 해석함수를 만들기 위해 사용됨




타원과 3차 블라쉬케 곱

  • 다음과 같은 3차의 블라쉬케 곱을 생각하자\[B(z)=z\frac{z-a}{1-\bar{a}z}\frac{z-b}{1-\bar{b}z}\]
  • 단위원 위의 점 \(\lambda\) 에 대하여, \(B(z)=\lambda\) 의 세 해를 \(z_ 1,z_ 2,z_ 3\) 로 두면, 세 직선 \(\overline{z_ 1z_ 2},\overline{z_ 2 z_ 3},\overline{z_ 1 z_ 3}\) 은 다음 타원에 접한다\[|w-a|+|w-b|=|1-\bar{a}b|\]
  • \(a=0.5,b=-0.4+0.4 i\) 로 두고, 다양한 \(\lambda\) 에 대하여 위의 결과를 적용하여 얻은 그림

블라쉬케 곱(Blaschke product)1.gif

  • [DPR2002] 참조




역사



메모



관련된 항목들

매스매티카 파일 및 계산 리소스


수학용어번역






사전 형태의 자료



리뷰논문, 에세이, 강의노트

  • Garcia, Stephan Ramon, Javad Mashreghi, and William T. Ross. “Finite Blaschke Products: A Survey.” arXiv:1512.05444 [math], December 16, 2015. http://arxiv.org/abs/1512.05444.

관련논문

  • Fletcher, Alastair. “Blaschke Products and Domains of Ellipticity.” arXiv:1408.2418 [math], August 11, 2014. http://arxiv.org/abs/1408.2418.
  • [DPR2002]Daepp, Ulrich, Pamela Gorkin, and Raymond Mortini. 2002. Ellipses and Finite Blaschke Products. The American Mathematical Monthly 109 (9) (November 1): 785-795. doi:10.2307/3072367.


노트

위키데이터

말뭉치

  1. Thus, Blaschke's theorem describes the sequences of zeros of all possible Blaschke products.[1]
  2. P.M. Tamrazov, "Conformal-metric theory of doubly connected domains and the generalized Blaschke product" Soviet Math.[1]
  3. We present four algorithms to determine whether or not a Blaschke product is a composition of two non-trivial Blaschke products and, if it is, the algorithms suggest what the composition must be.[2]
  4. The final algorithm looks at inverse images under the Blaschke product.[2]
  5. Blaschke products were introduced by Wilhelm Blaschke (1915).[3]
  6. This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields.[4]
  7. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products.[4]
  8. This book gathers the principal results about Blaschke products heretofore scattered in research papers over the past 70 years and provides an extensive bibliography of over 300 items.[5]
  9. It is hoped that research workers in and students of function theory will find the book a useful guide and reference to the subject of Blaschke products.[5]
  10. All examples of Blaschke products constructed so far to prove this result have their zeros located on a ray.[6]
  11. A Blaschke product always belongs to the set I of inner functions; it has norm 1 and radial limits of modulus 1 almost everywhere.[7]

소스

  1. ↑ 1.0 1.1 Encyclopedia of Mathematics
  2. ↑ 2.0 2.1 Decomposing finite Blaschke products
  3. ↑ Blaschke product
  4. ↑ 4.0 4.1 Finite Blaschke Products and Their Connections
  5. ↑ 5.0 5.1 Blaschke Products
  6. ↑ Girela , Peláez : On the derivative of infinite Blaschke products
  7. ↑ Some Lemmas on Interpolating Blaschke Products and a Correction

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'blaschke'}, {'LEMMA': 'product'}]
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