| Title:
|
Generalized Hermitean ultradistributions (English) |
| Author:
|
Andrade, C. |
| Author:
|
Loura, L. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
225-253 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we define, by duality methods, a space of ultradistributions $\G _\omega ' (\Bbb R ^N)$. This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two. The method used to construct $\Bbb G _\omega ' (\Bbb R ^N)$ led us to a detailed study, presented at the beginning of the paper, of the duals of infinite dimensional locally convex spaces that are inductive limits of finite dimensional subspaces. (English) |
| Keyword:
|
distribution |
| Keyword:
|
multipole series |
| Keyword:
|
Fourier transform |
| Keyword:
|
complex translation |
| Keyword:
|
ultradistribution |
| MSC:
|
32A25 |
| MSC:
|
32A45 |
| MSC:
|
46F05 |
| idZBL:
|
Zbl 1212.46058 |
| idMR:
|
MR2561304 |
| DOI:
|
10.21136/MB.2009.140658 |
| . |
| Date available:
|
2010-07-20T18:01:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140658 |
| . |
| Reference:
|
[1] Andrade, C. F.: Séries de Multipolos, Séries Formais e Transformação de Fourier.MSc Thesis, IST, Lisboa (1999). |
| Reference:
|
[2] Andrade, C. F.: Ultradistribuições Hermiteanas Generalizadas.PhD Thesis, FMH, Lisboa (2005). |
| Reference:
|
[3] Gordon, M.: Ultradistribuições Exponenciais.PhD Thesis, Universidade da Madeira, Funchal (2003). |
| Reference:
|
[4] Loura, L. C.: A space of generalized distributions.Czech. Math. J. 56 (2006), 543-558. Zbl 1164.46330, MR 2291755, 10.1007/s10587-006-0036-2 |
| Reference:
|
[5] Loura, L. C., Viegas, C. F.: Hermitean Ultradistributions.Port. Math. 55 (1998), 39-57. Zbl 0915.46039, MR 1614744 |
| Reference:
|
[6] Markushevich, A.: Theory of Functions of a Complex Variable (second ed.).Chelsea Pub. Co. (1977). MR 0444912 |
| Reference:
|
[7] Robertson, A. P., Robertson, W. J.: Topological Vector Spaces.Cambridge University Press, London (1964). Zbl 0123.30202, MR 0162118 |
| Reference:
|
[8] Schwartz, L.: Théorie des distributions.Hermann, Paris (1966). Zbl 0149.09501, MR 0209834 |
| Reference:
|
[9] Silvestre, A. L.: Os espaços de ultradistribuições $\mathcal{U}_W^{\prime}(\Omega)$ e $\mathcal{V}_W'(\Omega)$.MSc Thesis, IST, Lisboa (1996). |
| . |
