Geodesic
The Generalized D'Alembert Operator on Compactified Pseudo-Euclidean Space
Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 652-660

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It is proved that the D'Alembert operator in $\mathbb R^n$ with multidimensional time, bordered by operators of multiplication by some function, and subject to an acceptance condition at infinity is a self-adjoint operator with discrete spectrum. The spectrum and eigenfunctions are explicitly described.
Keywords: D'Alembert differential operator, self-adjoint operator, pseudo-Euclidean space, Kelvin transformation, Laplace operator, spherical function.
Mots-clés : conformal transformation group 
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     author = {A. S. Blagoveshchenskii},
     title = {The {Generalized} {D'Alembert} {Operator} on {Compactified} {Pseudo-Euclidean} {Space}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a1/}
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A. S. Blagoveshchenskii. The Generalized D'Alembert Operator on Compactified Pseudo-Euclidean Space. Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 652-660. http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a1/