A pointwise growth estimate for analytic functions in tubes
A class of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 growth estimate concerning these functions can be replaced by a pointwise growt...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171280000439 |
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| _version_ | 1832567265277509632 |
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| author | Richard D. Carmichael Elmer K. Hayashi |
| author_facet | Richard D. Carmichael Elmer K. Hayashi |
| author_sort | Richard D. Carmichael |
| collection | DOAJ |
| description | A class of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 growth estimate concerning these functions can be replaced by a pointwise growth estimate, and we obtain further new properties of these functions. Our analysis shows that these functions of Vladimirov are exactly the Hardy H2 class of functions corresponding to the tube TC. |
| format | Article |
| id | doaj-art-d08a55b0c6d74ebaa15431c7b0e24925 |
| 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-d08a55b0c6d74ebaa15431c7b0e249252025-02-03T01:02:04ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013357558110.1155/S0161171280000439A pointwise growth estimate for analytic functions in tubesRichard D. Carmichael0Elmer K. Hayashi1Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109, USADepartment of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109, USAA class of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 growth estimate concerning these functions can be replaced by a pointwise growth estimate, and we obtain further new properties of these functions. Our analysis shows that these functions of Vladimirov are exactly the Hardy H2 class of functions corresponding to the tube TC.http://dx.doi.org/10.1155/S0161171280000439analytic function in tubesHardy H2 spaceCauchy kernel and integralFourier-Laplace integral. |
| spellingShingle | Richard D. Carmichael Elmer K. Hayashi A pointwise growth estimate for analytic functions in tubes International Journal of Mathematics and Mathematical Sciences analytic function in tubes Hardy H2 space Cauchy kernel and integral Fourier-Laplace integral. |
| title | A pointwise growth estimate for analytic functions in tubes |
| title_full | A pointwise growth estimate for analytic functions in tubes |
| title_fullStr | A pointwise growth estimate for analytic functions in tubes |
| title_full_unstemmed | A pointwise growth estimate for analytic functions in tubes |
| title_short | A pointwise growth estimate for analytic functions in tubes |
| title_sort | pointwise growth estimate for analytic functions in tubes |
| topic | analytic function in tubes Hardy H2 space Cauchy kernel and integral Fourier-Laplace integral. |
| url | http://dx.doi.org/10.1155/S0161171280000439 |
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