Дудкін, МиколаКозак, Валентина2017-03-132017-03-132016Дудкін Микола Євгенович. Пряма спектральна задача з блочними матрицями типу Якобі, що відповідають сильній двовимірній проблемі моментів / Дудкін М. Є., Козак В. І. // Наукові записки НаУКМА : Фізико-математичні науки. - 2016. - Т. 178. - С. 16-22.https://ekmair.ukma.edu.ua/handle/123456789/11103In this article we propose an approach to the strong two-dimensional Hamburger moment problem based on the theory of generalized eigenvectors expansion for two commuting selfadjoint operators, that have inverse operators and the construction of corresponding block three-diagonals Jacobi type matrices. In this approach we at first prove the one-to-one correspondence between the strong two-dimensional Hamburger moment problem and corresponding block three-diagonals Jacobi type matrices by the use of the theory of eigenfunction expansion on generalized eigenvectors corresponding two commuting operators and their inverse operators. After this we show that operators generated by Jacobi type three-diagonals block matrix have the spectral measure corresponding to the moment representation. Such approach is proposed by Yu. M. Berezansky many years ago and gives the possibility to investigate the following moment problems: classical, trigonometric, complex, matrix and different many-dimensional analogs of them, including infinite-dimensional cases. At first the similar to above mentioned idea of the investigations of positive defined functions (named directed functionals) belongs to M. G. Krein (1946–1948). He has constructed the Hilbert space by means of investigated positive definite kernel and to natural operators in this space connected with investigated problem. All investigations are presented under not very burdening conditions, namely we suppose that the measure dρ(x, y) has compact support on the real plane R2, zero not belong to this support, such measure has all moments, the set xnym, m, n ∈ Z is liner independent with respect to dρ(x, y) and is total in L2(R2, dρ(x, y)). It means that we consider two bounded non-degenerated commuting selfadjoint operators such that have obligatory bounded inverse operators.Дослiдження симетричних матриць типу Якобi, що вiдповiдають сильнiй двовимiрнiй дiйснiй проблемi моментiв, започаткованi в, доповненi задачею про вiдновлення мiри за матрицями, полiномами другого роду та аналогом функцiї Вейля.ukматрицi типу Якобiсильна двовимiрна дiйсна проблема моментiвполiноми другого родуаналог функцiї Вейлястаттяof Jacobi type symmetric matricesthe strong two dimension real power moment problempolynomials of second orderanalog of Weyl functionArticle