The Cauchy-Stieltjes integrals in the theory of analytic functions
We study various Stieltjes integrals as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results hold for arbitrary bounded integrands that...
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| Published in: | Український математичний вісник |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/169377 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Cauchy-Stieltjes integrals in the theory of analytic functions / V.I. Ryazanov // Український математичний вісник. — 2017. — Т. 14, № 4. — С. 548-563. — Бібліогр.: 29 назв. — англ. |
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Ryazanov, V.I. 2020-06-11T17:55:22Z 2020-06-11T17:55:22Z 2017 The Cauchy-Stieltjes integrals in the theory of analytic functions / V.I. Ryazanov // Український математичний вісник. — 2017. — Т. 14, № 4. — С. 548-563. — Бібліогр.: 29 назв. — англ. 1810-3200 2010 MSC. 30С62, 31A05, 31A20, 31A25, 31B25, 35Q15; Secondary 30E25, 31C05, 34M50, 35F45. https://nasplib.isofts.kiev.ua/handle/123456789/169377 We study various Stieltjes integrals as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results hold for arbitrary bounded integrands that are differentiable a.e. and, in particular, for integrands of the class CBV (countably bounded variation). en Інститут прикладної математики і механіки НАН України Український математичний вісник The Cauchy-Stieltjes integrals in the theory of analytic functions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Cauchy-Stieltjes integrals in the theory of analytic functions |
| spellingShingle |
The Cauchy-Stieltjes integrals in the theory of analytic functions Ryazanov, V.I. |
| title_short |
The Cauchy-Stieltjes integrals in the theory of analytic functions |
| title_full |
The Cauchy-Stieltjes integrals in the theory of analytic functions |
| title_fullStr |
The Cauchy-Stieltjes integrals in the theory of analytic functions |
| title_full_unstemmed |
The Cauchy-Stieltjes integrals in the theory of analytic functions |
| title_sort |
cauchy-stieltjes integrals in the theory of analytic functions |
| author |
Ryazanov, V.I. |
| author_facet |
Ryazanov, V.I. |
| publishDate |
2017 |
| language |
English |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We study various Stieltjes integrals as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results hold for arbitrary bounded integrands that are differentiable a.e. and, in particular, for integrands of the class CBV (countably bounded variation).
|
| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/169377 |
| citation_txt |
The Cauchy-Stieltjes integrals in the theory of analytic functions / V.I. Ryazanov // Український математичний вісник. — 2017. — Т. 14, № 4. — С. 548-563. — Бібліогр.: 29 назв. — англ. |
| work_keys_str_mv |
AT ryazanovvi thecauchystieltjesintegralsinthetheoryofanalyticfunctions AT ryazanovvi cauchystieltjesintegralsinthetheoryofanalyticfunctions |
| first_indexed |
2025-12-07T18:10:35Z |
| last_indexed |
2025-12-07T18:10:35Z |
| _version_ |
1850874041116655616 |