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Abstract Differential Null-Equations

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Abstract

Let A be a closed linear operator in a Banach space, and let n ≥ 1 be an integer. If the resolvent λI − A)-1 is an entire function of λ∈ℂ of order < 1/n or of order 1/n and minimal type, then the equation dn u(t)/dt n=Au(t) has only the trivial solution u(t)≡0. An example for partial differential equations is given. Generalizations are indicated.

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  1. Moscow Institute of Engineering Physics, Russia

    I. V. Tikhonov

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  1. I. V. Tikhonov
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Tikhonov, I.V. Abstract Differential Null-Equations. Functional Analysis and Its Applications 38, 133–137 (2004). https://doi.org/10.1023/B:FAIA.0000034043.31169.4b

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  • DOI: https://doi.org/10.1023/B:FAIA.0000034043.31169.4b

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