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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 2, Pages 65–70 (Mi faa108)  

This article is cited in 1 scientific paper (total in 1 paper)

Abstract Differential Null-Equations

I. V. Tikhonov

Moscow Engineering Physics Institute (State University)

Abstract: 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.

Keywords: null-equation, closed linear operator, resolvent, entire function of minimal type, Pólya theorem

DOI: https://doi.org/10.4213/faa108

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English version:
Functional Analysis and Its Applications, 2004, 38:2, 133–137

Bibliographic databases:

UDC: 517.954
Received: 09.12.2002

Citation: I. V. Tikhonov, “Abstract Differential Null-Equations”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 65–70; Funct. Anal. Appl., 38:2 (2004), 133–137

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gefter S., Stulova T., “On Holomorphic Solutions of Some Implicit Linear Differential Equations in a Banach Space”, Modern Analysis and Applications: Mark Krein Centenary Conference, Operator Theory Advances and Applications, 191, 2009, 331–340  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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