Linear Relations as Generators of Semigroups of Operators
Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 175-192.

Voir la notice de l'article provenant de la source Math-Net.Ru

The theory of semigroups of bounded linear operators is based on the spectral theory of linear relations (multivalued linear operators), which act as generators of operator semigroups.
Keywords: semigroup, bounded linear operator, linear relation (multivalued linear operator), spectral theory, primitive generator of a semigroup, resolvent set of a linear relation, ergodic theorem, holomorphic function.
@article{MZM_2008_84_2_a1,
     author = {A. G. Baskakov},
     title = {Linear {Relations} as {Generators} of {Semigroups} of {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {175--192},
     publisher = {mathdoc},
     volume = {84},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a1/}
}
TY  - JOUR
AU  - A. G. Baskakov
TI  - Linear Relations as Generators of Semigroups of Operators
JO  - Matematičeskie zametki
PY  - 2008
SP  - 175
EP  - 192
VL  - 84
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a1/
LA  - ru
ID  - MZM_2008_84_2_a1
ER  - 
%0 Journal Article
%A A. G. Baskakov
%T Linear Relations as Generators of Semigroups of Operators
%J Matematičeskie zametki
%D 2008
%P 175-192
%V 84
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a1/
%G ru
%F MZM_2008_84_2_a1
A. G. Baskakov. Linear Relations as Generators of Semigroups of Operators. Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 175-192. http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a1/

[1] E. Khille, R. S. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1962 | MR | Zbl

[2] K.-J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math., 194, Springer-Verlag, New York, 2000 | MR | Zbl

[3] R. Cross, Multivalued Linear Operators, Monogr. Textbooks Pure Appl. Math., 213, Marcel Dekker, New York, 1998 | MR | Zbl

[4] A. Favini, A. Yagi, Degenerate Differential Equations in Banach Spaces, Monogr. Textbooks Pure Appl. Math., 215, Marcel Dekker, New York, 1999 | MR | Zbl

[5] A. G. Baskakov, K. I. Chernyshov, “Lineinye otnosheniya, differentsialnye vklyucheniya i vyrozhdennye polugruppy”, Funkts. analiz i ego pril., 36:4 (2002), 65–70 | MR | Zbl

[6] A. G. Baskakov, K. I. Chernyshov, “Spektralnaya teoriya lineinykh otnoshenii i vyrozhdennye polugruppy operatorov”, Matem. sb., 193:11 (2002), 3–42 | MR | Zbl

[7] R. Arens, “Operational calculus of linear relations”, Pacific J. Math., 11 (1961), 9–23 | MR | Zbl

[8] A. G. Baskakov, “Operatornye ergodicheskie teoremy i dopolnyaemye podprostranstva banakhovykh prostranstv”, Izv. vuzov. Matem., 1988, no. 11, 3–11 | MR | Zbl

[9] A. G. Baskakov, “Teoriya predstavlenii banakhovykh algebr, abelevykh grupp i polugrupp v spektralnom analize lineinykh operatorov”, SMFN, 9 (2004), 3–151 | MR | Zbl

[10] G. A. Sviridyuk, V. A. Fedorov, “Analiticheskie polugruppy s yadrami i lineinye uravneniya tipa Soboleva”, Sib. matem. zhurn., 36:5 (1995), 1130–1145 | MR | Zbl

[11] N. M. Gelfand, G. E. Shilov, Nekotorye voprosy teorii differentsialnykh uravnenii, Obobschennye funktsii, vyp. 3, Fizmatgiz, M., 1958 | MR | Zbl

[12] G. V. Demidenko, S. V. Uspenskii, Uravneniya i sistemy, ne razreshennye otnositelno starshei proizvodnoi, Nauchnaya kniga, Novosibirsk, 1998 | MR | Zbl

[13] N. E. Egorov, S. G. Pyatkov, S. V. Popov, Neklassicheskie differentsialno-operatornye uravneniya, Nauka, Novosibirsk, 2000 | MR | Zbl

[14] U. A. Anufrieva, I. V. Melnikova, “Osobennosti i regulyarizatsiya nekorrektnykh zadach Koshi s differentsialnymi operatorami”, SMFN, 14 (2005), 3–156 | MR | Zbl