On entire solutions of exponential type of some implicit linear differential-difference equation in a~Banach space
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 91-97
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $A$ be a closed linear operator on a Banach space with a possibly domain. Entire solutions of exponential type of the linear differential-difference equation $w'(z)=Aw(z-h)+f(z)$ are studied nondense. Assuming that operator $A$ has a bounded inverse, the well-posedness of this equation in a special space of entire $E$-valued function is proved.
@article{ZNSL_2013_416_a3,
author = {S. L. Gefter and T. E. Stulova},
title = {On entire solutions of exponential type of some implicit linear differential-difference equation in {a~Banach} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {91--97},
publisher = {mathdoc},
volume = {416},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a3/}
}
TY - JOUR AU - S. L. Gefter AU - T. E. Stulova TI - On entire solutions of exponential type of some implicit linear differential-difference equation in a~Banach space JO - Zapiski Nauchnykh Seminarov POMI PY - 2013 SP - 91 EP - 97 VL - 416 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a3/ LA - ru ID - ZNSL_2013_416_a3 ER -
%0 Journal Article %A S. L. Gefter %A T. E. Stulova %T On entire solutions of exponential type of some implicit linear differential-difference equation in a~Banach space %J Zapiski Nauchnykh Seminarov POMI %D 2013 %P 91-97 %V 416 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a3/ %G ru %F ZNSL_2013_416_a3
S. L. Gefter; T. E. Stulova. On entire solutions of exponential type of some implicit linear differential-difference equation in a~Banach space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 91-97. http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a3/