Commutant and Uniqueness of Solutions of Duhamel Equations

Tapdigoglu R. Torebek B.T.
March 2021 Springer

Bulletin of the Malaysian Mathematical Sciences Society
2021 #44 Issue 2 705 - 710 pp.

The Duhamel product for two suitable functions f and g is defined as follows: (f⊛g)(x)=ddx∫0xf(x-t)g(t)dt.We consider the integration operator J, Jf(x)=∫0xf(t)dt, on the Frechet space C^∞ of all infinitely differentiable functions in [0 , 1] and describe in terms of Duhamel operators its commutant. Also, we consider the Duhamel equation φ⊛ f= g and prove that it has a unique solution if and only if φ(0) ≠ 0.

Commutant , Duhamel equation , Duhamel product , Integration operator , Williamson theorem

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Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956, Istanbul, Turkey
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Faculty of Engineering and Natural Sciences
Al-Farabi Kazakh National University
Department of Mathematics: Analysis
Institute of Mathematics and Mathematical Modeling

10 лет помогаем публиковать статьи Международный издатель

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