Geodesic
Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 18-25

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

The spectral properties of operators constructed from a family of evolution operators are studied in Banach spaces of vector functions defined by a weight function of pre-exponential growth. Necessary and sufficient conditions for the invertibility of such operators are obtained in terms of exponential dichotomy. We prove a spectrum mapping theorem for semigroups of Howland difference operators generated by the operator under study.
Keywords: differential operator, weighted spaces of functions, spectral properties of operators, evolution operator, exponential dichotomy, Howland difference operator, Banach space, spectrum mapping theorem. 
M. S. Bichegkuev. Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 18-25. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a1/
@article{MZM_2014_95_1_a1,
     author = {M. S. Bichegkuev},
     title = {Spectral {Analysis} of {Differential} {Operators} with {Unbounded} {Operator} {Coefficients} in {Weighted} {Spaces} of {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {18--25},
     year = {2014},
     volume = {95},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a1/}
}
TY  - JOUR
AU  - M. S. Bichegkuev
TI  - Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions
JO  - Matematičeskie zametki
PY  - 2014
SP  - 18
EP  - 25
VL  - 95
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a1/
LA  - ru
ID  - MZM_2014_95_1_a1
ER  - 
%0 Journal Article
%A M. S. Bichegkuev
%T Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions
%J Matematičeskie zametki
%D 2014
%P 18-25
%V 95
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a1/
%G ru
%F MZM_2014_95_1_a1

[1] A. G. Baskakov, “Polugruppy raznostnykh operatorov v spektralnom analize lineinykh differentsialnykh operatorov”, Funkts. analiz i ego pril., 30:3 (1996), 1–11 | DOI | MR | Zbl

[2] M. S. Bichegkuev, “O spektre raznostnykh i differentsialnykh operatorov v vesovykh prostranstvakh”, Funkts. analiz i ego pril., 44:1 (2010), 80–83 | DOI | MR | Zbl

[3] A. G. Baskakov, “O korrektnosti lineinykh differentsialnykh operatorov”, Matem. sb., 190:3 (1999), 3–28 | DOI | MR | Zbl

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

[5] A. G. Baskakov, “Spektralnyi analiz differentsialnykh operatorov s neogranichennymi operatornymi koeffitsientami, raznostnye otnosheniya i polugruppy raznostnykh otnoshenii”, Izv. RAN. Ser. matem., 73:2 (2009), 3–68 | DOI | MR | Zbl

[6] M. S. Bichegkuev, “Lineinye raznostnye i differentsialnye operatory s neogranichennymi operatornymi koeffitsientami v vesovykh prostranstvakh”, Matem. zametki, 86:5 (2009), 673–680 | DOI | MR | Zbl

[7] M. S. Bichegkuev, “Ob usloviyakh razreshimosti raznostnykh uravnenii s nachalnym usloviem iz podprostranstva”, Sib. matem. zhurn., 51:4 (2010), 751–768 | MR | Zbl

[8] M. S. Bichegkuev, “Ob usloviyakh obratimosti raznostnykh i differentsialnykh operatorov v vesovykh prostranstvakh”, Izv. RAN. Ser. matem., 75:4 (2011), 3–20 | DOI | MR | Zbl

[9] A. G. Baskakov, “Lineinye differentsialnye operatory s neogranichennymi operatornymi koeffitsientami i polugruppy raznostnykh operatorov”, Matem. zametki, 59:6 (1996), 811–820 | DOI | MR | Zbl

[10] N. Van Minh, F. Räbiger, R. Schnaubelt, “Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equation on the half-line”, Integral Equations Operator Theory, 32:3 (1998), 332–353 | DOI | MR | Zbl

[11] C. Chicone, Yu. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, Math. Surveys Monogr., 70, Amer. Math. Soc., Provindence, RI, 1999 | MR | Zbl

[12] D. Todorov, Generalisation of Analogs of Theorems of Maizel and Pliss and Their Application in Shadowing Theory, arXiv: math.DS/1202.4338v1

[13] A. G. Baskakov, “Issledovanie lineinykh differentsialnykh uravnenii metodami spektralnoi teorii raznostnykh operatorov i lineinykh otnoshenii”, UMN, 68:1 (2013), 77–128 | DOI | MR | Zbl

[14] M. S. Bichegkuev, “K spektralnomu analizu raznostnykh i differentsialnykh operatorov v vesovykh prostranstvakh”, Matem. sb., 204:11 (2013), 3–20 | DOI