Two-dimensional half-strong real moment problem and the corresponding block matrices. Part II

  • M. E. Dudkin Nat. tech. University of Ukraine "KPI them. I. Sikorsky ”, Kyiv https://orcid.org/0000-0002-5554-182X
  • O. Yu. Dyuzhenkova Nat. tech. University of Ukraine "KPI them. I. Sikorsky ”, Kyiv

Abstract

UDC 517.9

We describe the direct and inverse spectral problems related to the block Jacobi type matrices that correspond to the two-dimensional half-strong real moment problem.
In particular, we obtain three matrices that have three-diagonal block structure and act in an $l_2$-like space as commuting self-adjoint operators, and two of them are mutually inverse.

References

Yu. M. Berezanskij, Разложения по собственным функциям самосопряженных операторов (Russian) [[Razlozheniya po sobstvenny`m funkcziyam samosopryazhenny`kh operatorov]], Nauk. dumka, Kiev, (1965); English translation: Amer. Math. Soc., Providence, R.I. (1968).

Yu. M. Berezanskiĭ, Yu. G. Kondratʹev, Спектральные методы в бесконечномерном анализе (Russian) [[Spectral methods in infinite-dimensional analysis]], Naukova Dumka, Kiev (1988).

Yu. M. Berezanskij, G. F. Us, Z. G. Sheftel, Функциональный анализ: Курс лекций (Russian) [[Funkczional`ny`j analiz: Kurs lekczij]], Vishha shk., Kiyiv (1990).

Yu. M. Berezansky, M. E. Dudkin, The direct and inverce spectral problems for the block Jacobi type unitary matrices, Methods Funct. Anal. and Topology, 11, № 4, 327 – 345 (2005).

Yu. M. Berezansky, M. E. Dudkin, Якобiєвi матрицi i проблема моментiв (Russian) [[Yakobiyevi matriczi i problema momentiv]], Praczi In-tu matematiki NAN Ukrayini, 105 (2019).

M. J. Cantero, L. Moral, L. Velázquez, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle, Linear Algebra and Appl., 362, 29 – 56 (2003), https://doi.org/10.1016/S0024-3795(02)00457-3

M. E. Dudkin, The exact inner structure of the block Jacobi type unitary matrices connected with the corresponding direct and inverse spectral problems matrices, Methods Funct. Anal. and Topology, 14, № 2, 168 – 176 (2008).

M. E. Dudkin, The inner structure of the Jacobi – Laurent matrix related to the strong Hamburger moment problem, Methods Funct. Anal. and Topology, 19, № 2, 97 – 107 (2013).

M. E. Dudkin, O. Yu. Dyuzhenkova, Двовимiрна дiйсна напiвсильна проблема мементiв та вiдповiднi блочнi матрицi, I (Russian) [[Two-dimensional half-strong real moment problem and the corresponding block matrices. Part I]], Ukr. mat. zhurn., 72, № 8, 1047 – 1063 (2020), https://doi.org/10.37863/umzh.v72i8.6062

Published
25.10.2020
How to Cite
Dudkin M. E., and Dyuzhenkova O. Y. “Two-Dimensional Half-Strong Real Moment Problem and the Corresponding Block Matrices. Part II”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 10, Oct. 2020, pp. 1335 -1364, doi:10.37863/umzh.v72i10.6231.
Section
Research articles