Geodesic
Some properties of operator exponent
Ural mathematical journal, Tome 4 (2018) no. 2, pp. 33-42

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

We study operators given by series, in particular, operators of the form $e^B=\sum\limits_{n=0}^{\infty}{B^n}/{n!},$ where $B$ is an operator acting in a Banach space $X$. A corresponding example is provided. In our future research, we will use these operators for introducing and studying functions of operators constructed (with the use of the Cauchy integral formula) on the basis of scalar functions and admitting a faster than power growth at infinity.
Keywords: Closed operator, Operator exponent, Multiplicative property. 
@article{UMJ_2018_4_2_a4,
     author = {Lyudmila F. Korkina and Mark A. Rekant},
     title = {Some properties of operator exponent},
     journal = {Ural mathematical journal},
     pages = {33--42},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a4/}
}
TY  - JOUR
AU  - Lyudmila F. Korkina
AU  - Mark A. Rekant
TI  - Some properties of operator exponent
JO  - Ural mathematical journal
PY  - 2018
SP  - 33
EP  - 42
VL  - 4
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a4/
LA  - en
ID  - UMJ_2018_4_2_a4
ER  - 
%0 Journal Article
%A Lyudmila F. Korkina
%A Mark A. Rekant
%T Some properties of operator exponent
%J Ural mathematical journal
%D 2018
%P 33-42
%V 4
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a4/
%G en
%F UMJ_2018_4_2_a4
Lyudmila F. Korkina; Mark A. Rekant. Some properties of operator exponent. Ural mathematical journal, Tome 4 (2018) no. 2, pp. 33-42. http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a4/