| Title:
|
Semi-groups of positive contraction operators (English) |
| Author:
|
Phillips, Ralph S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
12 |
| Issue:
|
2 |
| Year:
|
1962 |
| Pages:
|
294-313 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
47.50 |
| idZBL:
|
Zbl 0113.09901 |
| idMR:
|
MR0146675 |
| DOI:
|
10.21136/CMJ.1962.100517 |
| . |
| Date available:
|
2008-06-09T13:14:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/100517 |
| . |
| Reference:
|
[1] Garrett Birkhoff: Lattice theory.American Math. Soc. Coll. Publ. vol. 25, 1948. MR 0029876 |
| Reference:
|
[2] W. Feller: On the integro-differential equations of purely discontinuous Markoff processes.Trans. Amer. Math. Soc., vol. 48, 1940, 488-515. Zbl 0025.34704, MR 0002697, 10.1090/S0002-9947-1940-0002697-3 |
| Reference:
|
[3] W. Feller: On boundaries and lateral conditions for the Kolmogorov differential equations.Annals of Math. (2) vol. 65, 1957, 527-570. Zbl 0084.35503, MR 0090928, 10.2307/1970064 |
| Reference:
|
[4] E. Hille, R. S. Phillips: Functional analysis and semi-groups.Amer. Math. Soc. Coll. Publ., vol. 31, 1957. MR 0089373 |
| Reference:
|
[5] W. B. Jurkat: On semi-groups of positive matrices.Parts I and II, Scripta Math., vol. 24, 1959, 123-131 and 207-218. Zbl 0091.13002, MR 0121833 |
| Reference:
|
[6] S. Karlin, J. L. McGregor: The differential equations of birth-and-death processes and the Stieltjes moment problem.Trans. Amer. Math. Soc., vol. 85, 1957, 489-546. Zbl 0091.13801, MR 0091566, 10.1090/S0002-9947-1957-0091566-1 |
| Reference:
|
[7] Tosio Kato: On semi-groups generated by Kolmogoroff's differential equations.Jr. Math. Soc. of Japan, vol. 6, 1954, 1 - 15. MR 0062343 |
| Reference:
|
[8] David G. Kendall: Unitary dilations of one-parameter semi-groups of Markov transition operators, and the corresponding integral representations for Markov processes with a countable infinity of states.Proc. London Math. Soc., vol. 9, 1959, 417 - 431. MR 0116390 |
| Reference:
|
[9] M. G. Krein: The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications.Recueil. Math., vol. 20, 1947, 431 - 495. Zbl 0029.14103, MR 0024574 |
| Reference:
|
[10] W. Ledermann, G. E. H. Reuter: On differential equations for the transition probabilities of Markov processes with enumerably many states.Proc. Cambridge Phil. Soc., vol. 49, 1953, 247-262. MR 0053343 |
| Reference:
|
[11] G. Lumer, R. S. Phillips: Dissipative operators in Banach spaces.Pacific Jr. of Math., vol. 11, 1961, 679-698. MR 0132403, 10.2140/pjm.1961.11.679 |
| Reference:
|
[12] R. S. Phillips: Dissipative operators and hyperbolic systems of partial differential equations.Trans. Amer. Math. Soc., vol. 90, 1959, 193-254. MR 0104919, 10.1090/S0002-9947-1959-0104919-1 |
| Reference:
|
[13] R. S. Phillips: The extension of dual subspaces invariant under an algebra.Proc. of the International Symposium on Linear Spaces, Israel 1960, 366-398. MR 0133686 |
| Reference:
|
[14] G. E. H. Reuter: Denumerable Markov processes and the associated contraction semi-groups on $l_1$.Acta Math., vol. 97, 1957, 1 - 46. MR 0102123 |
| Reference:
|
[15] G. E. H. Reuter: Denumerable Markov processes. II.Jr. London Math. Soc., vol. 34, 1959, 81-91. Zbl 0089.13803, MR 0102124 |
| . |
