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Nonlocal Boundary-Value Problem for an Equation with Differentiation Operator z ∂/∂z in a Refined Sobolev Scale

Ilkiv, V. S. ; Strap, N. І. ; Volyanska, І. І.

Journal of mathematical sciences (New York, N.Y.), 2023-07, Vol.273 (6), p.885-900 [Periódico revisado por pares]

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Título:
Nonlocal Boundary-Value Problem for an Equation with Differentiation Operator z ∂/∂z in a Refined Sobolev Scale
Autor: Ilkiv, V. S. ; Strap, N. І. ; Volyanska, І. І.
Assuntos: Analysis ; Boundary value problems ; Complex variables ; Differential equations ; Differentiation ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Operators (mathematics)
É parte de: Journal of mathematical sciences (New York, N.Y.), 2023-07, Vol.273 (6), p.885-900
Descrição: We study a nonlocal boundary-value problem for a differential equation with operator of generalized differentiation B = z ∂/∂ z acting upon the functions of complex variable z . We establish the conditions of solvability of this problem in the scale of Hörmander spaces, which form the refined Sobolev scale of functions of one complex variable. The analyzed problem is ill posed in Hadamard's sense in the case of many operators of generalized differentiation, and its solvability depends on small denominators appearing in the construction of the solution. It is shown that, in the case of one variable, the corresponding denominators are not small and can be estimated from below by certain constants.
Editor: Cham: Springer International Publishing
Idioma: Inglês

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