The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
Lávička, Roman
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 115-135 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1998-01-01
Classification:  31C45,  35R15,  46C99,  46G05,  47F05 
@article{118991,
     author = {Roman L\'avi\v cka},
     title = {The L\'evy laplacian and differential operators of 2-nd order in Hilbert spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {115-135},
     zbl = {0945.47037},
     mrnumber = {1622994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118991}
}

Lávička, Roman. The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 115-135. http://gdmltest.u-ga.fr/item/118991/

Averbuch V.I.; Smoljanov O.G.; Fomin S.V. Generalization of functions and differential equations in linear spaces II., Differential operators and their Fourier transform (in Russian), Trudy Moskov. Mat. Obshch. 27 (1975), 247-262. (1975)

Daleckij J.L.; Fomin S.V. Measures and Differential Equations in Infinite Dimensional Spaces (in Russian), Nauka, Moscow, 1983. | MR 0720545

Mingarelli A.B.; Wang S. A maximum principle and related problems for a Laplacian in Hilbert space, Differential Equations and Dynamical Systems 1 (1993), 1 23-34. (1993) | MR 1385791 | Zbl 0885.35142

Gochberg I.C.; Krejn M.G. Introduction to the Theory of Linear Operators in Hilbert space (in Russian), Nauka, Moscow, 1965.

Lévy P. Problèmes Concrets d'analyse Fonctionnelle, Paris, Gauthier-Villars, 1951. | MR 0041346 | Zbl 0155.18201

Šilov G.E. On some questions of analysis in Hilbert space I. (in Russian), Functional Anal. Appl. 1 (1967), 2 81-90. (1967) | MR 0213916

Nemirovskij A.S.; Šilov G.E. On the axiomatic description of Laplace's operator for functions on Hilbert space (in Russian), Functional Anal. Appl. 3 (1969), 79-85. (1969) | MR 0253088

Sikirjavyj V.Ja. The invariant Laplace operator as an operator of pseudospherical differentiation (in Russian), Moscow Univ. Math. Bull. 3 (1972), 66-73. (1972) | MR 0305143