Geodesic
Cohomology of Sheaves of Fr\'echet Algebras and Spectral Theory
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 76-80.

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

We propose a holomorphic functional calculus for a noncommutative operator family generating a supernilpotent Lie subalgebra. This calculus extends Taylor's holomorphic functional calculus.
Keywords: functional calculus, Putinar spectrum, sheaf of Fréchet algebras, sheaf cohomology. 
@article{FAA_2005_39_3_a6,
     author = {A. A. Dosiev},
     title = {Cohomology of {Sheaves} of {Fr\'echet} {Algebras} and {Spectral} {Theory}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {76--80},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a6/}
}
TY  - JOUR
AU  - A. A. Dosiev
TI  - Cohomology of Sheaves of Fr\'echet Algebras and Spectral Theory
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2005
SP  - 76
EP  - 80
VL  - 39
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a6/
LA  - ru
ID  - FAA_2005_39_3_a6
ER  - 
%0 Journal Article
%A A. A. Dosiev
%T Cohomology of Sheaves of Fr\'echet Algebras and Spectral Theory
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2005
%P 76-80
%V 39
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a6/
%G ru
%F FAA_2005_39_3_a6
A. A. Dosiev. Cohomology of Sheaves of Fr\'echet Algebras and Spectral Theory. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 76-80. http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a6/

[1] Taylor J. L., Adv. in Math., 9 (1972), 183–252 | DOI | MR | Zbl

[2] Khelemskii A. Ya., Gomologiya v banakhovykh i topologicheskikh algebrakh, MGU, M., 1986 | MR

[3] Eschmeier J., Putinar M., Spectral decompositions and analytic sheaves, Clarendon Press, Oxford Univ. Press, 1996 | MR

[4] Godeman R., Algebraicheskaya topologiya i teoriya puchkov, IL, M., 1961

[5] Khërmander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR

[6] Dosiev A. A., Funkts. analiz i ego ppil., 34:4 (2000), 82–84 | DOI | MR | Zbl

[7] Dosiev A. A., J. Math. Sciences, 124:2 (2004), 4886–4908 | DOI | MR

[8] Khelemskii A. Ya., Banakhovy i polinormirovannye algebry: obschaya teoriya, predstavleniya, gomologii, Hauka, M., 1989 | MR

[9] Dosiev A. A., Funkts. analiz i ego ppil., 37:1 (2003), 73–77 | DOI | MR | Zbl

[10] Fainshtein A. S., J. Operator Theory, 29 (1993), 3–27 | MR | Zbl

[11] Turovskii Yu. V., Funkts. analiz i ego ppil., 18:2 (1984), 77–78 | MR | Zbl

[12] Dosiev A. A., J. Operator Theory, 48:3 (2002), 585–614 | MR