Generalized derivations and Fourier transform of polynomial ultradistributions |
|
| Author |
Institute of Mathematics
,Cracow University of Technology
,Cracow, Poland
|
| Abstract |
Algebras of symmetric ultradistributions on the spaces of
functions of infinitely many variables are investigated.
Linear representation of such algebras as
convolution algebras of symmetric tensor products are
constructed. Generalized derivations and Fourier transform
of such algebras are described.
|
| Keywords |
derivation, Fourier transform, polynomial ultradistribution
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| DOI |
doi:10.30970/ms.20.2.167-178
|
Reference |
1. Berezanski Yu.M. and Kondratiev Yu.G. Spectral Methods in Infinite-Dimensional Analysis, Naukova dumka, Kyiv, 1988.
2. Lopushansky O.V., Zagorodnyuk A.V. Hilbert spaces of analytic functions of infinitely many variables, Annales Polonici Mathematici, 81 (2003), № 2, 111–122. 3. Dineen S. Complex Analysis on Infinite Dimensional Spaces, Springer, 1999. 4. Grothendieck A. Produits tensoriels topologiques et espaces nucléaries, Mem. Amer. Math. Soc. 16 (1955). 5. Jarchow H. Locally Convex Spaces, B.G.Teubner, Stuttgart, 1981. 6. Hörmander L. The Analysis of Linear Partial Differential Operators, Springer, 1983. 7. Mityagin B.S. Nucl\'erit\'e et autres propri\'et\'es des espaces de type $s$, Trudy Mosk. Mat. Ob-va\/ 9 (1960), 317--328. 8. Pietsch A. Nukleare Localkonvexe Räume, Springer, 1965. 9. Shaefer H. Topological Vector Spaces, Springer, 1971. 10. Lions J.L., Magenes E. Problemes aux Limites non Homogenes et Applications, Paris: Dunod, v.3, 1970. 11. Sebastiano di Silva, On some classes of locally convex spaces, Matematika, 1 (1957), 60–67. 12. Grasela K. Ultraincreasing distributions of expotential type, Univ. Iagel. Acta Mathematica, (2003) (in print). |
| Pages |
167-178
|
| Volume |
20
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| Issue |
2
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| Year |
2003
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| Journal |
Matematychni Studii
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| Full text of paper | |
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