Geodesic
On solution to the simplest functional equation in curvilinear-band-type domain
Matematičeskie zametki SVFU, Tome 24 (2017) no. 4, pp. 87-95 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the functional equation $u(\xi + 1) - u(\xi) = d(\xi), \xi\in\Pi,$, in the region $\Pi\subset C$ of “curvilinear band” type. For sufficiently fast decreasing at infinity and holomorphic within the domain $\Pi$ functions $d(\xi)$ the existence of a holomorphic and bounded solution is shown, the uniqueness of the solutions is investigated. We also obtained precise estimates of the constructed solutions and its asymptotic behavior.
Keywords: semihyperbolic maps, functional equations, analytic classification. 
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     author = {P. A. Shaikhullina},
     title = {On solution to the simplest functional equation in curvilinear-band-type domain},
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P. A. Shaikhullina. On solution to the simplest functional equation in curvilinear-band-type domain. Matematičeskie zametki SVFU, Tome 24 (2017) no. 4, pp. 87-95. http://geodesic.mathdoc.fr/item/SVFU_2017_24_4_a7/

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