Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 207-218
Citer cet article
V. I. Burenkov. Formula for the differentiation of operator-valued functions depending on a parameter. Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 207-218. http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a10/
@article{MZM_1971_10_2_a10,
author = {V. I. Burenkov},
title = {Formula for the differentiation of operator-valued functions depending on a parameter},
journal = {Matemati\v{c}eskie zametki},
pages = {207--218},
year = {1971},
volume = {10},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a10/}
}
TY - JOUR
AU - V. I. Burenkov
TI - Formula for the differentiation of operator-valued functions depending on a parameter
JO - Matematičeskie zametki
PY - 1971
SP - 207
EP - 218
VL - 10
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a10/
LA - ru
ID - MZM_1971_10_2_a10
ER -
%0 Journal Article
%A V. I. Burenkov
%T Formula for the differentiation of operator-valued functions depending on a parameter
%J Matematičeskie zametki
%D 1971
%P 207-218
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a10/
%G ru
%F MZM_1971_10_2_a10
A study of the convergence of the differentiation formula $$ (f(A))'=f'(A)A'+\frac{f''(A)}{2!}[A'A]+\frac{f'''(A)}{3!}[[A'A]A]+\dots, $$ where $[XY]=XY-YX$, and $A=A(t)$ is a function of the real variable $t$ with values in a Banach algebra.
