Geodesic
Operator semigroups, cosine operator functions, and linear differential equations
Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", Tome 28 (1990), pp. 87-202
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

This survey presents a systematic exposition of the elements of the theory of operator semigroups (OS's) in Banach space from Hille–Yosida to the end of 1989. There is a parallel exposition of the theory of cosine operator functions (COF's). The paper contains the following divisions: Linear differential equations in Banach space, reduction of the Cauchy problem for second order equations to the Cauchy problem for first order equations, one-parameter OS's and COF's. differentiable OS's. analytic OS's. Fredholm OS's. positive OS's. stable OS's. spectral properties of OS's and COF's. compactness properties of OS's and COF's. uniformly continuous OS's and COF's. almost periodic OS's and COF's. uniformly bounded OS's and COF's. the theory of perturbations for OS's and COF's. ad joint OS's and COF's. 
@article{INTM_1990_28_a1,
     author = {V. V. Vasil'ev and S. G. Krein and S. I. Piskarev},
     title = {Operator semigroups, cosine operator functions, and linear differential equations},
     journal = {Itogi nauki i tehniki. Seri\^a, Matemati\v{c}eskij analiz},
     pages = {87--202},
     year = {1990},
     volume = {28},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTM_1990_28_a1/}
}
TY  - JOUR
AU  - V. V. Vasil'ev
AU  - S. G. Krein
AU  - S. I. Piskarev
TI  - Operator semigroups, cosine operator functions, and linear differential equations
JO  - Itogi nauki i tehniki. Seriâ, Matematičeskij analiz
PY  - 1990
SP  - 87
EP  - 202
VL  - 28
UR  - http://geodesic.mathdoc.fr/item/INTM_1990_28_a1/
LA  - ru
ID  - INTM_1990_28_a1
ER  - 
%0 Journal Article
%A V. V. Vasil'ev
%A S. G. Krein
%A S. I. Piskarev
%T Operator semigroups, cosine operator functions, and linear differential equations
%J Itogi nauki i tehniki. Seriâ, Matematičeskij analiz
%D 1990
%P 87-202
%V 28
%U http://geodesic.mathdoc.fr/item/INTM_1990_28_a1/
%G ru
%F INTM_1990_28_a1
V. V. Vasil'ev; S. G. Krein; S. I. Piskarev. Operator semigroups, cosine operator functions, and linear differential equations. Itogi nauki i tehniki. Seriâ, Matematičeskij analiz, Itogi Nauki i Tekhniki. Seriya "Matematicheskii Analiz", Tome 28 (1990), pp. 87-202. http://geodesic.mathdoc.fr/item/INTM_1990_28_a1/