Geodesic
Operational results in bi-orthogonal Hermite functions
Clemente Cesarano1 ; Claudio Fornaro1 ; Luis Vazquez2 ; Clemente Cesarano ; Claudio Fornaro ; Luis Vazquez
1Universita Telematica Internazionale Uninettuno, C.so Vittorio Emanuele II, 39,Rome
2Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense de Madrid, Ciudad Universitaria 28040, Madrid
Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 1, pp. 43-68 
Clemente Cesarano; Claudio Fornaro; Luis Vazquez; Clemente Cesarano; Claudio Fornaro; Luis Vazquez. Operational results in bi-orthogonal Hermite functions. Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 1, pp. 43-68. http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a4/
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     author = {Clemente Cesarano and Claudio Fornaro and Luis Vazquez and Clemente Cesarano and Claudio Fornaro and Luis Vazquez},
     title = { Operational results in bi-orthogonal {Hermite} functions},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {43--68},
     year = {2016},
     volume = {85},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

By starting from the concept of the orthogonality property related to the ordinary and generalized two-variable Hermite polynomials, we present some interesting results on the class of bi-orthogonal Hermite functions.The structure of these bi-orthogonal functions is based on the family of the two-index, two-variable Hermite polynomials of type $H_{m,n}(x; y)$ and their adjoint $G_{m,n}(x; y)$.We will also introduce a dierential representation of the operators acting on the above bi-orthogonal Hermite functions and we will derive some operational identities.