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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Official URL: https://dx.doi.org/10.1007/s40840-020-00972-1
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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