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CHARACTERIZATIONS OF RAPIDLY DECREASING GENERALIZED FUNCTIONS

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The well-known characterizations of the Schwartz space of rapidly decreasing functions is extended to new algebras of rapidly decreasing generalized functions.

Abstract

The well-known characterizations of the Schwartz space of rapidly decreasing functions is extended to new algebras of rapidly decreasing generalized functions.

참고문헌 (17)

  1. J. Alvarez, "Characterizations of the Schwartz space S and the Beurling-Bjorck space Sw", Cubo, 6(4), pp.167~183 (2004)
  2. K. Benmeriem, "Ultraregular generalized functions of Colombeau type", J. Math. Sci. Univ., 15(4), pp.427~447 (2008)
  3. H. A. Biagioni, "Generalized solutions to the Korteweg-de Vries and the regularized long-wave equations", SIAM J. Math. Anal., 23(4), pp.923~940 (1992)
  4. J. Chung, "Une caract´erisation de l’espace S de Schwartz", C. R. Acad. Sci. Paris S´er. I Math., 316(1), pp.23~25 (1993)
  5. J. F. Colombeau, "New Generalized Functions and Multiplication of Distributions" (1984), North-Holland Publishing Co.
  6. A. Delcroix, "Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity", J. Math. Anal. Appl., 327(1), pp.564~584 (2007)
  7. C. Garetto, "Pseudo-differential operators in algebras of generalized functions and global hypoellipticity", Acta Appl. Math., 80(2), pp.123~174 (2004)
  8. I. M. Gel’fand, "Generalized Functions, Vol. 2" (1967), Academic Press
  9. K. Gr¨ochenig, "Spaces of test functions via the STFT", J. Funct. Spaces Appl., 2(1), pp.25~53 (2004)
  10. M. Grosser, "Geometric Theory of Generalized Functions with Applications to General R" (2001), Kluwer Academic Publishers
  11. L. H¨ormander, "Distributions Theory And Fourier Analysis" (1983), Springer
  12. A. I. Kashpirovski, "Equality of the spaces S® ¯ and S®\S¯", Funct. Anal. Appl., 14, pp.129~ (1980)
  13. M. Oberguggenberger, "Regularity theory in Colombeau algebras", Bull. Cl. Sci. Math. Nat. Sci. Math., (31), pp.147~162 (2006)
  14. N. Ortner, "Applications of weighted D0 Lp -spaces to the convolution of distributions", Bull. Polish Acad. Sci. Math., 37(7), pp.579~595 (1989)
  15. Ya. V. Radyno, "The Fourier transformation in an algebra of new generalized functions", Dokl. Akad. Nauk, 327(1), pp.20~24 (1992)
  16. L. Schwartz, "Th´eorie des distributions" (1966), Hermann
  17. L. Volevich, "The Cauchy problem and related problems for convolution equations", Uspehi Mat. Nauk, 27(4(166)), pp.65~143 (1972)

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