Multipliers of Hankel transformable generalized functions

Jorge J. Betancor; Isabel Marrero

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 389-401
  • ISSN: 0010-2628

Abstract

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Let ℋ μ be the Zemanian space of Hankel transformable functions, and let ℋ μ ' be its dual space. In this paper ℋ μ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space O , also introduced by Zemanian, is completely characterized as the set of multipliers of ℋ μ and of ℋ μ ' . Certain topologies are considered on 𝒪 , and continuity properties of the multiplication operation with respect to those topologies are discussed.

How to cite

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Betancor, Jorge J., and Marrero, Isabel. "Multipliers of Hankel transformable generalized functions." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 389-401. <http://eudml.org/doc/247367>.

@article{Betancor1992,
abstract = {Let $\mathcal \{H\}_\{\mu \}$ be the Zemanian space of Hankel transformable functions, and let $\mathcal \{H\}^\{\prime \}_\{\mu \}$ be its dual space. In this paper $\mathcal \{H\}_\{\mu \}$ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space $\text\{O\}$, also introduced by Zemanian, is completely characterized as the set of multipliers of $\mathcal \{H\}_\{\mu \}$ and of $\mathcal \{H\}^\{\prime \}_\{\mu \}$. Certain topologies are considered on $\mathcal \{O\}$, and continuity properties of the multiplication operation with respect to those topologies are discussed.},
author = {Betancor, Jorge J., Marrero, Isabel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {multipliers; generalized functions; Hankel transformation; Zemanian space of Hankel transformable functions; nuclear; Schwartz; Montel; reflexive; multiplication operation},
language = {eng},
number = {3},
pages = {389-401},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Multipliers of Hankel transformable generalized functions},
url = {http://eudml.org/doc/247367},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Betancor, Jorge J.
AU - Marrero, Isabel
TI - Multipliers of Hankel transformable generalized functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 389
EP - 401
AB - Let $\mathcal {H}_{\mu }$ be the Zemanian space of Hankel transformable functions, and let $\mathcal {H}^{\prime }_{\mu }$ be its dual space. In this paper $\mathcal {H}_{\mu }$ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space $\text{O}$, also introduced by Zemanian, is completely characterized as the set of multipliers of $\mathcal {H}_{\mu }$ and of $\mathcal {H}^{\prime }_{\mu }$. Certain topologies are considered on $\mathcal {O}$, and continuity properties of the multiplication operation with respect to those topologies are discussed.
LA - eng
KW - multipliers; generalized functions; Hankel transformation; Zemanian space of Hankel transformable functions; nuclear; Schwartz; Montel; reflexive; multiplication operation
UR - http://eudml.org/doc/247367
ER -

References

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  1. Barros-Neto J., An Introduction to the Theory of Distributions, R.E. Krieger Publishing Company, Malabar, Florida, 1981. Zbl0512.46040
  2. Horvath J., Topological Vector Spaces and Distributions, Vol. 1, Addison-Wesley, Reading, Massachusetts, 1966. MR0205028
  3. Pietsch A., Nuclear Locally Convex Spaces, Springer-Verlag, Berlin, 1972. Zbl0308.47024MR0350360
  4. Treves F., Topological Vector Spaces, Distributions, and Kernels, Academic Press, New York, 1967. Zbl1111.46001MR0225131
  5. Wong Y.-Ch., Schwartz Spaces, Nuclear Spaces, and Tensor Products, Lecture Notes in Math. 726, Springer-Verlag, Berlin, 1979. Zbl0413.46001MR0541034
  6. Zemanian A.H., The Hankel transformation of certain distributions of rapid growth, SIAM J. Appl. Math. 14 (1966), 678-690. (1966) Zbl0154.13804MR0211211
  7. Zemanian A.H., Generalized Integral Transformations, Interscience, New York, 1968. Zbl0643.46029MR0423007

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