A Survey on the Integral Means Spectrum for Conformal Mappings
The present survey is devoted to the description of the results about estimates of the integral means in various classes of analytic functions. Great importance is given to the boundary properties of conformal mappings. The systematic results on the estimation of the integral means spectrum and the...
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Kazan Federal University
2015-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/portal/docs/F1324576722/157_2_phys_mat_9.pdf |
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| _version_ | 1841562997548384256 |
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| author | I.R. Kayumov |
| author_facet | I.R. Kayumov |
| author_sort | I.R. Kayumov |
| collection | DOAJ |
| description | The present survey is devoted to the description of the results about estimates of the integral means in various classes of analytic functions. Great importance is given to the boundary properties of conformal mappings. The systematic results on the estimation of the integral means spectrum and the well-known law of the iterated logarithm for conformal mappings, which was proven by N.G. Makarov in 1985, were the basic mathematical tools for this study. Precise estimates of the integral means in various subclasses of univalent functions are described. Estimates of the integral means spectrum in the class of functions mapping the exterior of the unit disk onto the attraction basins of the infinity of algebraic polynomials are presented. |
| format | Article |
| id | doaj-art-6e5bd0fdec9b4a60b2f9588cafe1417a |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-6e5bd0fdec9b4a60b2f9588cafe1417a2025-01-03T00:27:42ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982015-06-011572104115A Survey on the Integral Means Spectrum for Conformal MappingsI.R. Kayumov0Kazan Federal University, Kazan, 420008 RussiaThe present survey is devoted to the description of the results about estimates of the integral means in various classes of analytic functions. Great importance is given to the boundary properties of conformal mappings. The systematic results on the estimation of the integral means spectrum and the well-known law of the iterated logarithm for conformal mappings, which was proven by N.G. Makarov in 1985, were the basic mathematical tools for this study. Precise estimates of the integral means in various subclasses of univalent functions are described. Estimates of the integral means spectrum in the class of functions mapping the exterior of the unit disk onto the attraction basins of the infinity of algebraic polynomials are presented.https://kpfu.ru/portal/docs/F1324576722/157_2_phys_mat_9.pdfconformal mappingsintegral means spectrumharmonic measure |
| spellingShingle | I.R. Kayumov A Survey on the Integral Means Spectrum for Conformal Mappings Учёные записки Казанского университета: Серия Физико-математические науки conformal mappings integral means spectrum harmonic measure |
| title | A Survey on the Integral Means Spectrum for Conformal Mappings |
| title_full | A Survey on the Integral Means Spectrum for Conformal Mappings |
| title_fullStr | A Survey on the Integral Means Spectrum for Conformal Mappings |
| title_full_unstemmed | A Survey on the Integral Means Spectrum for Conformal Mappings |
| title_short | A Survey on the Integral Means Spectrum for Conformal Mappings |
| title_sort | survey on the integral means spectrum for conformal mappings |
| topic | conformal mappings integral means spectrum harmonic measure |
| url | https://kpfu.ru/portal/docs/F1324576722/157_2_phys_mat_9.pdf |
| work_keys_str_mv | AT irkayumov asurveyontheintegralmeansspectrumforconformalmappings AT irkayumov surveyontheintegralmeansspectrumforconformalmappings |