Geodesic
Abstract Differential Null-Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 65-70

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

Let $A$ be a closed linear operator in a Banach space, and let $n\ge1$ be an integer. If the resolvent $(\lambda I-A)^{-1}$ is an entire function of $\lambda\in\mathbb{C}$ of order $1/n$ or of order $1/n$ and minimal type, then the equation $d^nu(t)/dt^n=Au(t)$ has only the trivial solution $u(t)\equiv0$. An example for partial differential equations is given. Generalizations are indicated.
Mots-clés : null-equation
Keywords: closed linear operator, resolvent, entire function of minimal type, Pólya theorem. 
@article{FAA_2004_38_2_a5,
     author = {I. V. Tikhonov},
     title = {Abstract {Differential} {Null-Equations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {65--70},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a5/}
}
TY  - JOUR
AU  - I. V. Tikhonov
TI  - Abstract Differential Null-Equations
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2004
SP  - 65
EP  - 70
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a5/
LA  - ru
ID  - FAA_2004_38_2_a5
ER  - 
%0 Journal Article
%A I. V. Tikhonov
%T Abstract Differential Null-Equations
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2004
%P 65-70
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a5/
%G ru
%F FAA_2004_38_2_a5
I. V. Tikhonov. Abstract Differential Null-Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 2, pp. 65-70. http://geodesic.mathdoc.fr/item/FAA_2004_38_2_a5/