Commutant and uniqueness of solutions of Duhamel equations

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Tapdıgoğlu, Ramiz and Torebek, Berikbol T. (2021) Commutant and uniqueness of solutions of Duhamel equations. Bulletin of the Malaysian Mathematical Sciences Society, 44 (2). pp. 705-710. ISSN 0126-6705 (Print) 2180-4206 (Online)

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Abstract

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.
Item Type: Article
Uncontrolled Keywords: Commutant; Duhamel equation; Duhamel product; Integration operator; Williamson theorem
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ramiz Tapdıgoğlu
Date Deposited: 19 Aug 2022 14:55
Last Modified: 19 Aug 2022 14:55
URI: https://research.sabanciuniv.edu/id/eprint/43249

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