Generalized Hermitean ultradistributions
Mathematica Bohemica (2009)
- Volume: 134, Issue: 3, page 225-253
- ISSN: 0862-7959
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topAndrade, C., and Loura, L.. "Generalized Hermitean ultradistributions." Mathematica Bohemica 134.3 (2009): 225-253. <http://eudml.org/doc/38090>.
@article{Andrade2009,
abstract = {In this paper we define, by duality methods, a space of ultradistributions $_\omega ^\{\prime \} (\mathbb \{R\} ^N)$. 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 $\mathbb \{G\} _\omega ^\{\prime \} (\mathbb \{R\} ^N)$ 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.},
author = {Andrade, C., Loura, L.},
journal = {Mathematica Bohemica},
keywords = {distribution; multipole series; Fourier transform; complex translation; ultradistribution; distribution; multipole series; Fourier transform; complex translation},
language = {eng},
number = {3},
pages = {225-253},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized Hermitean ultradistributions},
url = {http://eudml.org/doc/38090},
volume = {134},
year = {2009},
}
TY - JOUR
AU - Andrade, C.
AU - Loura, L.
TI - Generalized Hermitean ultradistributions
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 3
SP - 225
EP - 253
AB - In this paper we define, by duality methods, a space of ultradistributions $_\omega ^{\prime } (\mathbb {R} ^N)$. 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 $\mathbb {G} _\omega ^{\prime } (\mathbb {R} ^N)$ 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.
LA - eng
KW - distribution; multipole series; Fourier transform; complex translation; ultradistribution; distribution; multipole series; Fourier transform; complex translation
UR - http://eudml.org/doc/38090
ER -
References
top- Andrade, C. F., Séries de Multipolos, Séries Formais e Transformação de Fourier, MSc Thesis, IST, Lisboa (1999). (1999)
- Andrade, C. F., Ultradistribuições Hermiteanas Generalizadas, PhD Thesis, FMH, Lisboa (2005). (2005)
- Gordon, M., Ultradistribuições Exponenciais, PhD Thesis, Universidade da Madeira, Funchal (2003). (2003)
- Loura, L. C., 10.1007/s10587-006-0036-2, Czech. Math. J. 56 (2006), 543-558. (2006) Zbl1164.46330MR2291755DOI10.1007/s10587-006-0036-2
- Loura, L. C., Viegas, C. F., Hermitean Ultradistributions, Port. Math. 55 (1998), 39-57. (1998) Zbl0915.46039MR1614744
- Markushevich, A., Theory of Functions of a Complex Variable (second ed.), Chelsea Pub. Co. (1977). (1977) MR0444912
- Robertson, A. P., Robertson, W. J., Topological Vector Spaces, Cambridge University Press, London (1964). (1964) Zbl0123.30202MR0162118
- Schwartz, L., Théorie des distributions, Hermann, Paris (1966). (1966) Zbl0149.09501MR0209834
- Silvestre, A. L., Os espaços de ultradistribuições e , MSc Thesis, IST, Lisboa (1996). (1996)
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