On tempered convolution operators
Commentationes Mathematicae Universitatis Carolinae (1994)
- Volume: 35, Issue: 1, page 1-7
- ISSN: 0010-2628
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topAbdullah, Saleh. "On tempered convolution operators." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 1-7. <http://eudml.org/doc/247570>.
@article{Abdullah1994,
abstract = {In this paper we show that if $S$ is a convolution operator in $\text\{S\}^\{\,\, \prime \}$, and $S\ast \text\{S\}^\{\,\, \prime \}=\text\{S\}^\{\,\, \prime \}$, then the zeros of the Fourier transform of $S$ are of bounded order. Then we discuss relations between the topologies of the space $\text\{O\}_c^\{\, \prime \}$ of convolution operators on $\text\{S\}^\{\,\, \prime \}$. Finally, we give sufficient conditions for convergence in the space of convolution operators in $\text\{S\}^\{\,\, \prime \}$ and in its dual.},
author = {Abdullah, Saleh},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {tempered distribution; convolution operator; Fourier transform; convergence of sequences; space of convolution operators; tempered distribution; convergence of sequences; convolution operator; zeros of the Fourier transform},
language = {eng},
number = {1},
pages = {1-7},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On tempered convolution operators},
url = {http://eudml.org/doc/247570},
volume = {35},
year = {1994},
}
TY - JOUR
AU - Abdullah, Saleh
TI - On tempered convolution operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 1
EP - 7
AB - In this paper we show that if $S$ is a convolution operator in $\text{S}^{\,\, \prime }$, and $S\ast \text{S}^{\,\, \prime }=\text{S}^{\,\, \prime }$, then the zeros of the Fourier transform of $S$ are of bounded order. Then we discuss relations between the topologies of the space $\text{O}_c^{\, \prime }$ of convolution operators on $\text{S}^{\,\, \prime }$. Finally, we give sufficient conditions for convergence in the space of convolution operators in $\text{S}^{\,\, \prime }$ and in its dual.
LA - eng
KW - tempered distribution; convolution operator; Fourier transform; convergence of sequences; space of convolution operators; tempered distribution; convergence of sequences; convolution operator; zeros of the Fourier transform
UR - http://eudml.org/doc/247570
ER -
References
top- Barros-Neto J., An Introduction to the Theory of Distributions, Marcel Dekker, New York, 1973. Zbl0512.46040MR0461128
- Grothendieck A., Produits Tensoriels Topologiques et Espaces Nucleaires, Memoirs of the Amer. Math. Soc. 16, Providence, 1966. Zbl0123.30301MR1609222
- Hörmander L., On the division of distributions by polynomials, Ark. Mat., Band 3, No. 53 (1958), 555-568. (1958) MR0124734
- Horvath J., Topological Vector Spaces and Distributions, Vol. I, Addison-Wesley, Mass., 1966. Zbl0143.15101MR0205028
- Keller K., Some convergence properties of distributions, Studia Mathematica 77 (1983), 87-93. (1983) MR0738046
- Schwartz L., Théorie des Distributions, Hermann, Paris, 1966. Zbl0962.46025MR0209834
- Sznajder S., Zielezny Z., On some properties of convolution operators in and , J. Math. Anal. Appl. 65 (1978), 543-554. (1978) MR0510469
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