Пряма спектральна задача з блочними матрицями типу Якобі, що відповідають сильній двовимірній проблемі моментів

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dc.contributor.authorДудкін, Микола
dc.contributor.authorКозак, Валентина
dc.date.accessioned2017-03-13T08:12:52Z
dc.date.available2017-03-13T08:12:52Z
dc.date.issued2016
dc.descriptionIn 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.en_US
dc.description.abstractДослiдження 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.uk_UA
dc.identifier.citationДудкін 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.uk_UA
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/11103
dc.language.isoukuk_UA
dc.relation.sourceНаукові записки НаУКМА: Фізико-математичні наукиuk_UA
dc.statuspublished earlieruk_UA
dc.subjectматрицi типу Якобiuk_UA
dc.subjectсильна двовимiрна дiйсна проблема моментiвuk_UA
dc.subjectполiноми другого родуuk_UA
dc.subjectаналог функцiї Вейляuk_UA
dc.subjectстаттяuk_UA
dc.subjectof Jacobi type symmetric matricesen_US
dc.subjectthe strong two dimension real power moment problemen_US
dc.subjectpolynomials of second orderen_US
dc.subjectanalog of Weyl functionen_US
dc.titleПряма спектральна задача з блочними матрицями типу Якобі, що відповідають сильній двовимірній проблемі моментівuk_UA
dc.title.alternativeThe investigations of Jacobi type symmetric matrices related to the strong two dimension real power moment problemen_US
dc.typeArticleuk_UA
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