Integral representations for harmonic and biharmonic functions in the unit ball (in Russian)
In the paper an analytical solution of the analytic continuation problem in the unit N-dimensional ball by its values on the inner sphere is found. A generalization of the classical Poisson formula is obtained. A solution of the similar analytic continuation problem for certain known operator expres...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2013-04-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/texts/2013/39_1/67-73.pdf |
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| _version_ | 1849409763393142784 |
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| author | O. E. Yaremko |
| author_facet | O. E. Yaremko |
| author_sort | O. E. Yaremko |
| collection | DOAJ |
| description | In the paper an analytical solution of the analytic continuation problem in the unit N-dimensional ball by its values on the inner sphere is found. A generalization of the classical Poisson formula is obtained. A solution of the similar analytic continuation problem for certain known operator expressions of a given potential on the inner sphere is obtained. A new result of the moment problem making a connection between the moment problem on a segment and on the half-axis is found. |
| format | Article |
| id | doaj-art-97c314a6f5464a83917d801ebad646d3 |
| institution | Kabale University |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2013-04-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-97c314a6f5464a83917d801ebad646d32025-08-20T03:35:23ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342013-04-013916773Integral representations for harmonic and biharmonic functions in the unit ball (in Russian)O. E. YaremkoIn the paper an analytical solution of the analytic continuation problem in the unit N-dimensional ball by its values on the inner sphere is found. A generalization of the classical Poisson formula is obtained. A solution of the similar analytic continuation problem for certain known operator expressions of a given potential on the inner sphere is obtained. A new result of the moment problem making a connection between the moment problem on a segment and on the half-axis is found.http://matstud.org.ua/texts/2013/39_1/67-73.pdfextension problemPoisson formulamoment problemsbiharmonic functionharmonic functionunit ball |
| spellingShingle | O. E. Yaremko Integral representations for harmonic and biharmonic functions in the unit ball (in Russian) Математичні Студії extension problem Poisson formula moment problems biharmonic function harmonic function unit ball |
| title | Integral representations for harmonic and biharmonic functions in the unit ball (in Russian) |
| title_full | Integral representations for harmonic and biharmonic functions in the unit ball (in Russian) |
| title_fullStr | Integral representations for harmonic and biharmonic functions in the unit ball (in Russian) |
| title_full_unstemmed | Integral representations for harmonic and biharmonic functions in the unit ball (in Russian) |
| title_short | Integral representations for harmonic and biharmonic functions in the unit ball (in Russian) |
| title_sort | integral representations for harmonic and biharmonic functions in the unit ball in russian |
| topic | extension problem Poisson formula moment problems biharmonic function harmonic function unit ball |
| url | http://matstud.org.ua/texts/2013/39_1/67-73.pdf |
| work_keys_str_mv | AT oeyaremko integralrepresentationsforharmonicandbiharmonicfunctionsintheunitballinrussian |