A functional model for a family of operators induced by Laguerre operator
Ra'ed, Hatamleh
Archivum Mathematicum, Tome 039 (2003), p. 11-25 / Harvested from Czech Digital Mathematics Library

The paper generalizes the instruction, suggested by B. Sz.-Nagy and C. Foias, for operatorfunction induced by the Cauchy problem \[ T_t : \left\lbrace \begin{array}{ll}th^{\prime \prime }(t) + (1-t)h^\prime (t) + Ah(t)=0\\ h(0) = h_0 (th^\prime )(0)=h_1 \end{array}\right.\] A unitary dilatation for $T_t$ is constructed in the present paper. then a translational model for the family $T_t$ is presented using a model construction scheme, suggested by Zolotarev, V., [3]. Finally, we derive a discrete functional model of family $T_t$ and operator $A$ applying the Laguerre transform \[ f(x)\rightarrow \int _0^\infty f(x) \,P_n(x)\,e^{-x} dx \] where $P_n(x)$ are Laguerre polynomials [6, 7]. We show that the Laguerre transform is a straightening transform which transfers the family $T_t$ (which is not semigroup) into discrete semigroup $e^{-itn}$.

Publié le : 2003-01-01
Classification:  34G99,  47A40,  47A48,  47A50,  47D06,  47E05
@article{107850,
     author = {Hatamleh Ra'ed},
     title = {A functional model for a family of operators induced by Laguerre operator},
     journal = {Archivum Mathematicum},
     volume = {039},
     year = {2003},
     pages = {11-25},
     zbl = {1109.47308},
     mrnumber = {1982208},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107850}
}
Ra'ed, Hatamleh. A functional model for a family of operators induced by Laguerre operator. Archivum Mathematicum, Tome 039 (2003) pp. 11-25. http://gdmltest.u-ga.fr/item/107850/

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