A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle
Let C be the unit circle {z: |z| = 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L_2[−1,1] is greater than 1/8.
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2019-05-01
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| Series: | Проблемы анализа |
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| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=6030&lang=ru |
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Article |
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doaj-b76f1996a73a4fbfa4ca2e1ce8485efd2021-07-02T05:15:11ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322019-05-018(26)2677210.15393/j3.art.2019.6030A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circleKomarov M. A.0Vladimir State UniversityLet C be the unit circle {z: |z| = 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L_2[−1,1] is greater than 1/8.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=6030&lang=rulogarithmic derivativeC-polynomialsimplest fractionnormunit circle |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Komarov M. A. |
| spellingShingle |
Komarov M. A. A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle Проблемы анализа logarithmic derivative C-polynomial simplest fraction norm unit circle |
| author_facet |
Komarov M. A. |
| author_sort |
Komarov M. A. |
| title |
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle |
| title_short |
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle |
| title_full |
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle |
| title_fullStr |
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle |
| title_full_unstemmed |
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle |
| title_sort |
lower bound for the l_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle |
| publisher |
Petrozavodsk State University |
| series |
Проблемы анализа |
| issn |
2306-3424 2306-3432 |
| publishDate |
2019-05-01 |
| description |
Let C be the unit circle {z: |z| = 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L_2[−1,1] is greater than 1/8. |
| topic |
logarithmic derivative C-polynomial simplest fraction norm unit circle |
| url |
http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=6030&lang=ru |
| work_keys_str_mv |
AT komarovma alowerboundforthel211normofthelogarithmicderivativeofpolynomialswithzerosontheunitcircle AT komarovma lowerboundforthel211normofthelogarithmicderivativeofpolynomialswithzerosontheunitcircle |
| _version_ |
1721338906154106880 |