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

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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. 
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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/

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