Mean-periodic functions
We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn)). This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis' work on partial...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1980-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171280000154 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552482733031424 |
|---|---|
| author | Carlos A. Berenstein B. A. Taylor |
| author_facet | Carlos A. Berenstein B. A. Taylor |
| author_sort | Carlos A. Berenstein |
| collection | DOAJ |
| description | We show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn)). This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables. |
| format | Article |
| id | doaj-art-197299f78a3e4a77b10dee6a511faf71 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-197299f78a3e4a77b10dee6a511faf712025-02-03T05:58:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013219923510.1155/S0161171280000154Mean-periodic functionsCarlos A. Berenstein0B. A. Taylor1Department of Mathematics, University of Maryland, College Park, Maryland 20742, USADepartment of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USAWe show that any mean-periodic function f can be represented in terms of exponential-polynomial solutions of the same convolution equation f satisfies, i.e., u∗f=0(μ∈E′(ℝn)). This extends to n-variables the work of L. Schwartz on mean-periodicity and also extends L. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.http://dx.doi.org/10.1155/S0161171280000154mean-periodic functionsinterpolation by entire functions. |
| spellingShingle | Carlos A. Berenstein B. A. Taylor Mean-periodic functions International Journal of Mathematics and Mathematical Sciences mean-periodic functions interpolation by entire functions. |
| title | Mean-periodic functions |
| title_full | Mean-periodic functions |
| title_fullStr | Mean-periodic functions |
| title_full_unstemmed | Mean-periodic functions |
| title_short | Mean-periodic functions |
| title_sort | mean periodic functions |
| topic | mean-periodic functions interpolation by entire functions. |
| url | http://dx.doi.org/10.1155/S0161171280000154 |
| work_keys_str_mv | AT carlosaberenstein meanperiodicfunctions AT bataylor meanperiodicfunctions |