References
- Catuogno , P. , Molina , S. and Olivera , C. 2007 . On Hermite expansions and products of tempered distributions . Integral Transforms Spec. Funct. , 18 : 233 – 243 .
- Colombeau , J. F. 1984 . “ New Generalized Functions and Multiplication of Distributions ” . North-Holland, Amsterdam
- Dattoli , G. , Srivastava , H. M. and Khan , S. 2005 . Operational versus Lie-algebraic methods and the theory of multi-variable Hermite polynomials . Integral Transforms Spec. Funct. , 16 : 81 – 91 .
- Dattoli , G. , Srivastava , H. M. and Zhukovsky , K. 2005 . Orthogonality properties of the Hermite and related polynomials . J. Comput. Appl. Math. , 182 : 165 – 172 .
- Dattoli , G. , Srivastava , H. M. and Zhukovsky , K. 2007 . Operational methods and differential equations with applications to initial-value problem . Appl. Math. Comput. , 184 : 979 – 1001 .
- Ding , X. Q. and Luo , P. Z. 2004 . Generalized weak functions . Acta Math. Sci. , 24B : 691 – 697 .
- Ding , X. Q. and Wang , Z. 2005 . Multiplication of weak functions . Acta Math. Sci. , 25B : 569 – 576 .
- Doha , E. H. 2004 . On the connection coefficients and recurrence relations arising from expansions in series of Hermite polynomials . Integral Transforms Spec. Funct. , 15 : 13 – 29 .
- Fish , B. 2004 . “ Some non-commutative products of distributions ” . In Publ. Math. Vol. 64 , 253 – 239 . Debrecen
- Fish , B. and Tas , K. 2006 . On the non-commutative neutrix product of the distributions x and x . Acta Math. Sin. , 22 : 1639 – 1644 . (English Series)
- Khabibrakhamov , I. K. and Summers , D. 1998 . The use of generalized Laguerre polynomials in spectral methods for nonlinear differential equations . Comput. Math. Appl. , 36 : 65 – 70 .
- Nedeljkov , M. , Pilipovic , S. and Scarpalezos , D. 1992 . “ The Linear Theory of Colombeau Generalized Functions, Pitman Research Notes in Mathematics ” . Vol. 259 , Longman, Harlow
- Oberguggenberger , M. 1998 . “ Multiplication of Distributions and Applications to Partial Differential Equations, Pitman Research Notes in Mathematics ” . Vol. 385 , Harlow : Longman .
- Radha , R. and Thangavelu , S. 2004 . Hardy's inequalities for Hermite and Laguerre expansions . Proc. Amer. Math. Soc. , 132 : 3525 – 3536 .
- Schwartz , L. 1954 . “ Sur l’ impossibilite de la multiplication des distributions ” . In C.R. Acad. Sci Vol. 239 , 847 – 848 . Paris
- Thangavelu , S. 1993 . “ Lectures on Hermite and Laguerre Expansions ” . In Math. Notes , Vol. 42 , Princeton, NJ : Princeton University Press .