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Uniqueness solution to the inverse spectral problem with distributed parameters on the graph-star. / Жабко, Алексей Петрович; Нуртазина, Карлыгаш Бегахметовна; Провоторов, Вячеслав Васильевич.
в: Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления, Том 16, № 2, 2020, стр. 129-143.Результаты исследований: Научные публикации в периодических изданиях › статья
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TY - JOUR
T1 - Uniqueness solution to the inverse spectral problem with distributed parameters on the graph-star.
AU - Жабко, Алексей Петрович
AU - Нуртазина, Карлыгаш Бегахметовна
AU - Провоторов, Вячеслав Васильевич
PY - 2020
Y1 - 2020
N2 - In the space of piecewise smooth functions on a star graph, the question of the uniqueness of the recovery of the differential operator of a boundary value problem from its spectral characteristics is analyzed. The uniqueness of the recovery of the coefficient in a differential expression and the constant in the boundary conditions of a boundary value problem from spectral data is considered - a set of eigenvalues and a set of norms of the operator’s eigenfunctions. The operator of the boundary value problem has a singularity generated by the structure of the graph: differential expression is defined on the interior parts of all the edges of the graph, and in the interior node of the graph, where the differential expression loses its meaning, there is a generalized condition of Kirchhoff - the condition of agreement (the condition of conjugating). A spectral approach is used, which is based on the spectral properties of the elliptical operator: the analyticity of Green’s function of the boundary value problem on the
AB - In the space of piecewise smooth functions on a star graph, the question of the uniqueness of the recovery of the differential operator of a boundary value problem from its spectral characteristics is analyzed. The uniqueness of the recovery of the coefficient in a differential expression and the constant in the boundary conditions of a boundary value problem from spectral data is considered - a set of eigenvalues and a set of norms of the operator’s eigenfunctions. The operator of the boundary value problem has a singularity generated by the structure of the graph: differential expression is defined on the interior parts of all the edges of the graph, and in the interior node of the graph, where the differential expression loses its meaning, there is a generalized condition of Kirchhoff - the condition of agreement (the condition of conjugating). A spectral approach is used, which is based on the spectral properties of the elliptical operator: the analyticity of Green’s function of the boundary value problem on the
KW - differential operator
KW - graph
KW - inverse spectral problem
KW - spectral characteristics
KW - uniqueness solution
KW - граф
KW - дифференциальный оператор
KW - единственность решения
KW - обратная спектральная задача
KW - спектральные характеристики
KW - differential operator
KW - graph
KW - inverse spectral problem
KW - spectral characteristics
KW - uniqueness solution
KW - граф
KW - дифференциальный оператор
KW - единственность решения
KW - обратная спектральная задача
KW - спектральные характеристики
M3 - Article
VL - 16
SP - 129
EP - 143
JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
SN - 1811-9905
IS - 2
ER -
ID: 78589966