대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제23권2호
  • /
  • Pages.201-209
  • /
  • 2008
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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LAGUERRE EXPANSIONS AND PRODUCTS OF DISTRIBUTIONS

  • Catuogno, Pedro (Departamento de Mathematica Universidade Estadual de Campinas) ;
  • Martinez, Federico (Departamento de Matematicas Facultad de Ciencias Exactas Y Naturales Universidad Nacional de Mar Del Plata) ;
  • Molina, Sandra (Departamento de Matematicas Facultad de Ciencias Exactas Y Naturales Universidad Nacional de Mar Del Plata)
  • 발행 : 2008.04.30
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초록

In this paper we introduce two products of tempered distributions with positive support. These products are based in the Laguerre representation of distributions. We calculate some products as, $[{\delta}]x^{\lambda}_+={\delta}[x^{\lambda}_+]=0\;and\;[x^{\lambda}_+]x^{\mu}_+=x^{{\lambda}+{\mu}}_+$ for appropriate ${\lambda}$ and ${\mu}$.

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참고문헌

  1. P. Catuogno, S. Molina, and C. Olivera, On Hermite espansions and products of tempered distributions, Integral Transform and Special Functions 18 (2007), 233-244 https://doi.org/10.1080/10652460601041169
  2. A. Duran, Laguerre expansions of tempered distributions and generalized functions, Journal of Mathematical Analysis and its Applications 150 (1990), 166-180 https://doi.org/10.1016/0022-247X(90)90205-T
  3. M. Guillemot-Teissiers, Developpments des distributions en series de fonctions orthogonales: Series de Legendre et de Laguerre, Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 519-573
  4. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, 1994
  5. N. Lebedev, Special Function and their Applications, Dover Publications, 1972
  6. M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Math. Series 259. Ed Longman Science and Technology, 1993
  7. N. Saad and R. Hall, Closed-form Sums for Some Pertubations Series Involving Hypergeometric Functions, Journal of Physics A: Mathematical and General 35 (2002), 4105-4123 https://doi.org/10.1088/0305-4470/35/18/308
  8. L. Schwartz, Theorie des Distributions. Hermann, Paris, 1966
  9. L. Schwartz Sur l'impossibilite de la multiplication des distributions, C. R. Acad. Sci. Paris 239 (1954), 847-848
  10. S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Princeton University Press, 1993