Stieltjes transforms on new generalized functions
We introduce a Stieltjes transform on the equivalence classes of a new generalized function which has been successfully developed by Colombeau. Subsets of rapid descent test functions, 𝒮(ℝn), as well as tempered distributions, 𝒮′(ℝn), are used to preserve Fourier analysis techniques.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004252 |
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| _version_ | 1832549339797389312 |
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| author | John Schmeelk |
| author_facet | John Schmeelk |
| author_sort | John Schmeelk |
| collection | DOAJ |
| description | We introduce a Stieltjes transform on the equivalence classes of
a new generalized function which has been successfully developed
by Colombeau. Subsets of rapid descent test functions, 𝒮(ℝn), as well as tempered distributions, 𝒮′(ℝn), are used to preserve Fourier analysis techniques. |
| format | Article |
| id | doaj-art-e14c46ed22bb47798a205ebf4057514b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e14c46ed22bb47798a205ebf4057514b2025-02-03T06:11:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125642142710.1155/S0161171201004252Stieltjes transforms on new generalized functionsJohn Schmeelk0Department of Mathematical Sciences, Virginia Commonwealth University, Richmond 23284-2014, VA, USAWe introduce a Stieltjes transform on the equivalence classes of a new generalized function which has been successfully developed by Colombeau. Subsets of rapid descent test functions, 𝒮(ℝn), as well as tempered distributions, 𝒮′(ℝn), are used to preserve Fourier analysis techniques.http://dx.doi.org/10.1155/S0161171201004252 |
| spellingShingle | John Schmeelk Stieltjes transforms on new generalized functions International Journal of Mathematics and Mathematical Sciences |
| title | Stieltjes transforms on new generalized functions |
| title_full | Stieltjes transforms on new generalized functions |
| title_fullStr | Stieltjes transforms on new generalized functions |
| title_full_unstemmed | Stieltjes transforms on new generalized functions |
| title_short | Stieltjes transforms on new generalized functions |
| title_sort | stieltjes transforms on new generalized functions |
| url | http://dx.doi.org/10.1155/S0161171201004252 |
| work_keys_str_mv | AT johnschmeelk stieltjestransformsonnewgeneralizedfunctions |