Stability in Generalized Functions
We consider the following additive functional equation with 𝑛-independent variables: ∑𝑓(𝑛𝑖=1𝑥𝑖∑)=𝑛𝑖=1𝑓(𝑥𝑖∑)+𝑛𝑖=1𝑓(𝑥𝑖−𝑥𝑖−1) in the spaces of generalized functions. Making use of the heat kernels, we solve the general solutions and the stability problems of the above equation in the spaces of tempered...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/502903 |
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| author | Young-Su Lee |
| author_facet | Young-Su Lee |
| author_sort | Young-Su Lee |
| collection | DOAJ |
| description | We consider the following additive functional equation with 𝑛-independent variables: ∑𝑓(𝑛𝑖=1𝑥𝑖∑)=𝑛𝑖=1𝑓(𝑥𝑖∑)+𝑛𝑖=1𝑓(𝑥𝑖−𝑥𝑖−1) in the spaces of generalized functions. Making use of the heat kernels, we solve the general solutions and the stability problems of the above equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the mollifiers, we extend these results to the space of distributions. |
| format | Article |
| id | doaj-art-49faa8033df74a048ebe98b608c10be9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-49faa8033df74a048ebe98b608c10be92025-02-03T01:26:29ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/502903502903Stability in Generalized FunctionsYoung-Su Lee0Department of Mathematics, Sogang University, Seoul 121-741, Republic of KoreaWe consider the following additive functional equation with 𝑛-independent variables: ∑𝑓(𝑛𝑖=1𝑥𝑖∑)=𝑛𝑖=1𝑓(𝑥𝑖∑)+𝑛𝑖=1𝑓(𝑥𝑖−𝑥𝑖−1) in the spaces of generalized functions. Making use of the heat kernels, we solve the general solutions and the stability problems of the above equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the mollifiers, we extend these results to the space of distributions.http://dx.doi.org/10.1155/2011/502903 |
| spellingShingle | Young-Su Lee Stability in Generalized Functions Abstract and Applied Analysis |
| title | Stability in Generalized Functions |
| title_full | Stability in Generalized Functions |
| title_fullStr | Stability in Generalized Functions |
| title_full_unstemmed | Stability in Generalized Functions |
| title_short | Stability in Generalized Functions |
| title_sort | stability in generalized functions |
| url | http://dx.doi.org/10.1155/2011/502903 |
| work_keys_str_mv | AT youngsulee stabilityingeneralizedfunctions |