Geodesic
On the uniqueness of solutions of Duhamel equations
Filomat, Tome 36 (2022) no. 11, p. 3891

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DOI

We consider the Duhamel equation φ ⊛ f = in the subspace C ∞ xy = f ∈ C ∞ ([0, 1] × [0, 1]) : f x, y = F xy for some F ∈ C ∞ [0, 1] of the space C ∞ ([0, 1] × [0, 1]) and prove that if φ xy=0 0, then this equation is uniquely solvable in C ∞ xy. The commutant of the restricted double integration operator W xy f xy := x 0 y 0 f (tτ) dτdt on C ∞ xy is also described. Some other related questions are also discussed.
DOI : 10.2298/FIL2211891T
Classification : 46E35, 47B38
Keywords: The Duhamel product, Duhamel equation, double integration operator, commutant 
Ramiz Tapdigoglu. On the uniqueness of solutions of Duhamel equations. Filomat, Tome 36 (2022) no. 11, p. 3891 . doi: 10.2298/FIL2211891T
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     author = {Ramiz Tapdigoglu},
     title = {On the uniqueness of solutions of {Duhamel} equations},
     journal = {Filomat},
     pages = {3891 },
     year = {2022},
     volume = {36},
     number = {11},
     doi = {10.2298/FIL2211891T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2211891T/}
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