INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS
Let 𝑛 >= 2, 𝑉_𝑟(R^𝑛) be the set of functions with zero integrals over all balls in R^𝑛 of radius 𝑟. Various interpolation problems for the class 𝑉_𝑟(R^𝑛) are studied. In the case when the set of interpolation nodes is finite, we solve the interpolation problem under general conditions. For the pr...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2021-08-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10751&lang=ru |
| _version_ | 1811335770672201728 |
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| author | V. V. Volchkov Vit. V. Volchkov |
| author_facet | V. V. Volchkov Vit. V. Volchkov |
| author_sort | V. V. Volchkov |
| collection | DOAJ |
| description | Let 𝑛 >= 2, 𝑉_𝑟(R^𝑛) be the set of functions with zero integrals over all balls in R^𝑛 of radius 𝑟. Various interpolation problems for the class 𝑉_𝑟(R^𝑛) are studied. In the case when the set of interpolation nodes is finite, we solve the interpolation problem under general conditions. For the problems with infinite set of
nodes, some sufficient conditions of solvability are founded. Note that an essential condition is that the definition of the class 𝑉_𝑟(R^𝑛) involves integration over balls. For instance, it can be shown that the analogues of our results in which the class of functions is defined using zero integrals over all shifts of a fixed parallelepiped in R^𝑛 do not hold true. |
| first_indexed | 2024-04-13T17:29:59Z |
| format | Article |
| id | doaj.art-d331d5b073254c539a220e2ffda80d23 |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-04-13T17:29:59Z |
| publishDate | 2021-08-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-d331d5b073254c539a220e2ffda80d232022-12-22T02:37:37ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322021-08-0110 (28)312914010.15393/j3.art.2021.10751INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANSV. V. Volchkov0Vit. V. Volchkov1Donetsk National University 24 Universitetskaya str., Donetsk 283001, RussiaDonetsk National University 24 Universitetskaya str., Donetsk 283001, RussiaLet 𝑛 >= 2, 𝑉_𝑟(R^𝑛) be the set of functions with zero integrals over all balls in R^𝑛 of radius 𝑟. Various interpolation problems for the class 𝑉_𝑟(R^𝑛) are studied. In the case when the set of interpolation nodes is finite, we solve the interpolation problem under general conditions. For the problems with infinite set of nodes, some sufficient conditions of solvability are founded. Note that an essential condition is that the definition of the class 𝑉_𝑟(R^𝑛) involves integration over balls. For instance, it can be shown that the analogues of our results in which the class of functions is defined using zero integrals over all shifts of a fixed parallelepiped in R^𝑛 do not hold true.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10751&lang=ruinterpolation problemsspherical meansmean periodicity |
| spellingShingle | V. V. Volchkov Vit. V. Volchkov INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS Проблемы анализа interpolation problems spherical means mean periodicity |
| title | INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS |
| title_full | INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS |
| title_fullStr | INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS |
| title_full_unstemmed | INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS |
| title_short | INTERPOLATION PROBLEMS FOR FUNCTIONS WITH ZERO BALL MEANS |
| title_sort | interpolation problems for functions with zero ball means |
| topic | interpolation problems spherical means mean periodicity |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=10751&lang=ru |
| work_keys_str_mv | AT vvvolchkov interpolationproblemsforfunctionswithzeroballmeans AT vitvvolchkov interpolationproblemsforfunctionswithzeroballmeans |