Properties of mappings of scalar functions to operator functions of a linear closed operator
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 153-165
Voir la notice de l'article provenant de la source Math-Net.Ru
We study classes of functions of a linear injective operator constructed on the basis of corresponding scalar functions that are analytic in domains lying outside some angle $\Delta$ with vertex at zero containing the negative real semiaxis. The functions have power estimates for the modulus at infinity and, possibly, at zero. It is assumed that the regular set of the operator contains an angle with vertex at zero lying in $\Delta$ and containing the negative real semiaxis and that an asymptotic estimate for the norm of the resolvent is known at zero and infinity. This paper continues the authors' studies of the properties of operator functions from relevant classes. Under the assumption of boundedness of the inverse operator, we propose a new sufficient condition for an equality related to raising a power of an operator to a power.
Keywords:
linear closed operator; functions of an operator; multiplicative property; invertibility.
@article{TIMM_2015_21_1_a14,
author = {L. F. Korkina and M. A. Rekant},
title = {Properties of mappings of scalar functions to operator functions of a linear closed operator},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {153--165},
publisher = {mathdoc},
volume = {21},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a14/}
}
TY - JOUR AU - L. F. Korkina AU - M. A. Rekant TI - Properties of mappings of scalar functions to operator functions of a linear closed operator JO - Trudy Instituta matematiki i mehaniki PY - 2015 SP - 153 EP - 165 VL - 21 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a14/ LA - ru ID - TIMM_2015_21_1_a14 ER -
%0 Journal Article %A L. F. Korkina %A M. A. Rekant %T Properties of mappings of scalar functions to operator functions of a linear closed operator %J Trudy Instituta matematiki i mehaniki %D 2015 %P 153-165 %V 21 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a14/ %G ru %F TIMM_2015_21_1_a14
L. F. Korkina; M. A. Rekant. Properties of mappings of scalar functions to operator functions of a linear closed operator. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 153-165. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a14/