Geodesic
An operator generalization of the logarithmic residue theorem and the theorem of Rouch\'e
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 603-625

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

We obtain the operator generalization of the theorem on the logarithmic residue for meromorphic operator-functions. The proof of the generalization is based on a theorem concerning a special factorization of a meromorphic operator-function at a point. This theorem also allows us to generalize, to the case of meromorphic operator-functions, the formula of M. V. Keldysh for the principal part of the resolvent as well as several other theorems. A definition is given for the multiplicity of a pole for a meromorphic operator-function. The basic properties of the multiplicity of a pole are proved, and also a generalization of the Rouché theorem. Bibliography: 16 titles. 
@article{SM_1971_13_4_a7,
     author = {I. Ts. Gokhberg and E. I. Sigal},
     title = {An operator generalization of the logarithmic residue theorem and the theorem of {Rouch\'e}},
     journal = {Sbornik. Mathematics},
     pages = {603--625},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_4_a7/}
}
TY  - JOUR
AU  - I. Ts. Gokhberg
AU  - E. I. Sigal
TI  - An operator generalization of the logarithmic residue theorem and the theorem of Rouch\'e
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 603
EP  - 625
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1971_13_4_a7/
LA  - en
ID  - SM_1971_13_4_a7
ER  - 
%0 Journal Article
%A I. Ts. Gokhberg
%A E. I. Sigal
%T An operator generalization of the logarithmic residue theorem and the theorem of Rouch\'e
%J Sbornik. Mathematics
%D 1971
%P 603-625
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1971_13_4_a7/
%G en
%F SM_1971_13_4_a7
I. Ts. Gokhberg; E. I. Sigal. An operator generalization of the logarithmic residue theorem and the theorem of Rouch\'e. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 603-625. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a7/