Abstract
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).
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