Geodesic
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 115-135

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We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.
Classification : 31C45, 35R15, 46C99, 46G05, 47F05
Keywords: Lévy laplacian; maximum principle; Dirichlet and Poisson problem 
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     author = {L\'avi\v{c}ka, Roman},
     title = {The {L\'evy} laplacian and differential operators of 2-nd order in {Hilbert} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {115--135},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {1998},
     mrnumber = {1622994},
     zbl = {0945.47037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998__39_1_a12/}
}
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Lávička, Roman. The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 115-135. http://geodesic.mathdoc.fr/item/CMUC_1998__39_1_a12/