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Interpolation in multidimensions, a convenient finite-dimensional matrix representation of the (partial) differential operators, and some applications (1993)

Calogero, F.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 34 (1993), S. 4704-4724

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: An extension to multidimensions of (a generalized notion of) Lagrangian interpolation is used to introduce finite-dimensional matrix representations of the (partial) differential operators. This makes it possible to extend to a multidimensional environment various results which were obtained in the past by exploiting such a representation in a one-dimensional context. Some such applications are outlined: the construction of remarkable matrices, convenient techniques to solve numerically eigenvalue problems and differential equations in multidimensions, and the manufacture of solvable "many-body'' dynamical systems in multidimensional spaces (some instances of such systems are exhibited).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530366

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