A Tauberian theorem for distributions

Jiří Čížek; Jiří Jelínek

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 479-488
  • ISSN: 0010-2628

Abstract

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The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.

How to cite

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Čížek, Jiří, and Jelínek, Jiří. "A Tauberian theorem for distributions." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 479-488. <http://eudml.org/doc/247929>.

@article{Čížek1996,
abstract = {The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.},
author = {Čížek, Jiří, Jelínek, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Tauberian theorem; distribution; convolution; Fourier transform; Tauberian theorem; distribution; convolution; Fourier transform},
language = {eng},
number = {3},
pages = {479-488},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A Tauberian theorem for distributions},
url = {http://eudml.org/doc/247929},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Čížek, Jiří
AU - Jelínek, Jiří
TI - A Tauberian theorem for distributions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 479
EP - 488
AB - The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.
LA - eng
KW - Tauberian theorem; distribution; convolution; Fourier transform; Tauberian theorem; distribution; convolution; Fourier transform
UR - http://eudml.org/doc/247929
ER -

References

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  1. Dierolf P., Voigt J., Convolutions and S ' -convolutions of distributions, Collect. Math. 29 (1978), 185-196. (1978) MR0565276
  2. Ganelius T.H., Tauberian Remainder Theorems, Lecture Notes in Math. 232 (1971), 75. (1971) Zbl0222.40001MR0499898
  3. Grothendieck A., Produits Tensoriels topologiques et espaces nuclaires, Memoirs of the AMS 16 (1966), 196+140. (1966) MR0075539
  4. Hardy G.H., Divergent Series, Oxford (1949). (1949) Zbl0032.05801MR0030620
  5. Horvth J., Topological Vector Spaces and Distributions, Addison-Wesley Publishing Company (1966), 449. (1966) 
  6. Hirata, Ogata, On the exchange formula for distributions, J. Sci. Hiroshima Univ. Ser. A 22 (1958), 147-152. (1958) MR0110014
  7. Itano M., On the theory of multiplicative products of distributions, J. Sci. Hiroshima Univ. Ser. A-I 30 (1966), 151-181. (1966) MR0209835
  8. Kamiński A., Convolution, product and Fourier transform of distributions, Stud. Math 74 (1982), 83-96. (1982) MR0675434
  9. Oberguggenberger M., Multiplication of Distributions and Applications to Partial Differential Equations, Institut für Mathematik und Geometrie, Universität Innsbruck, Austria, 1992, p. 312. Zbl0818.46036MR1187755
  10. Pilipović S., Stanković B., Wiener Tauberian theorems for distributions, J. London Math. Society, Second Series 47.3 (1993), 507-515. (1993) MR1214912
  11. Shiraishi R., On the definition of convolutions for distributions, J. Sci. Hiroshima Univ. Ser. A 23.1 (April 1959), 19-32. (April 1959) Zbl0091.28601MR0114122
  12. Schwartz L., Theorie des distributions I, II, Herman, Paris (1957). (1957) MR0209834
  13. Wiener N., Tauberian theorems, Ann. of Math. (2) 33 (1932), 1-100. (1932) Zbl0005.25003MR1503035

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