| Title:
|
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces (English) |
| Author:
|
Lávička, Roman |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
115-135 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lévy laplacian |
| Keyword:
|
maximum principle |
| Keyword:
|
Dirichlet and Poisson problem |
| MSC:
|
31C45 |
| MSC:
|
35R15 |
| MSC:
|
46C99 |
| MSC:
|
46G05 |
| MSC:
|
47F05 |
| idZBL:
|
Zbl 0945.47037 |
| idMR:
|
MR1622994 |
| . |
| Date available:
|
2009-01-08T18:39:28Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118991 |
| . |
| Reference:
|
[1] 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. |
| Reference:
|
[2] Daleckij J.L., Fomin S.V.: Measures and Differential Equations in Infinite Dimensional Spaces (in Russian).Nauka, Moscow, 1983. MR 0720545 |
| Reference:
|
[3] 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. Zbl 0885.35142, MR 1385791 |
| Reference:
|
[4] Gochberg I.C., Krejn M.G.: Introduction to the Theory of Linear Operators in Hilbert space (in Russian).Nauka, Moscow, 1965. |
| Reference:
|
[5] Lévy P.: Problèmes Concrets d'analyse Fonctionnelle.Paris, Gauthier-Villars, 1951. Zbl 0155.18201, MR 0041346 |
| Reference:
|
[6] Šilov G.E.: On some questions of analysis in Hilbert space I. (in Russian).Functional Anal. Appl. 1 (1967), 2 81-90. MR 0213916 |
| Reference:
|
[7] 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. MR 0253088 |
| Reference:
|
[8] Sikirjavyj V.Ja.: The invariant Laplace operator as an operator of pseudospherical differentiation (in Russian).Moscow Univ. Math. Bull. 3 (1972), 66-73. MR 0305143 |
| . |
