Commutant and uniqueness of solutions of Duhamel equations

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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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

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