Strong boundedness of analytic functions in tubes
Certain classes of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions g′. We further give a direct proof...
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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171279000028 |
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| _version_ | 1832562718077353984 |
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| author | Richard D. Carmichael |
| author_facet | Richard D. Carmichael |
| author_sort | Richard D. Carmichael |
| collection | DOAJ |
| description | Certain classes of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions g′. We further give a direct proof that each analytic function attains the Fourier transform of its spectral function as distributional boundary value in the strong (and weak) topology of g′. |
| format | Article |
| id | doaj-art-1333dfa90593401896337808ed95d751 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1333dfa90593401896337808ed95d7512025-02-03T01:21:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-0121152810.1155/S0161171279000028Strong boundedness of analytic functions in tubesRichard D. Carmichael0Department of Mathematics, Iowa State University, Ames 50011, Iowa, USACertain classes of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions g′. We further give a direct proof that each analytic function attains the Fourier transform of its spectral function as distributional boundary value in the strong (and weak) topology of g′.http://dx.doi.org/10.1155/S0161171279000028analytic function in tubesstrong boundednesstempered distributionsdistributional boundary value. |
| spellingShingle | Richard D. Carmichael Strong boundedness of analytic functions in tubes International Journal of Mathematics and Mathematical Sciences analytic function in tubes strong boundedness tempered distributions distributional boundary value. |
| title | Strong boundedness of analytic functions in tubes |
| title_full | Strong boundedness of analytic functions in tubes |
| title_fullStr | Strong boundedness of analytic functions in tubes |
| title_full_unstemmed | Strong boundedness of analytic functions in tubes |
| title_short | Strong boundedness of analytic functions in tubes |
| title_sort | strong boundedness of analytic functions in tubes |
| topic | analytic function in tubes strong boundedness tempered distributions distributional boundary value. |
| url | http://dx.doi.org/10.1155/S0161171279000028 |
| work_keys_str_mv | AT richarddcarmichael strongboundednessofanalyticfunctionsintubes |