Titlebook: Jacobi Matrices and the Moment Problem; Yurij M. Berezansky,Mykola E. Dudkin Book 2023 The Editor(s) (if applicable) and The Author(s), un

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The Strong Moment Problem,In this chapter, we present the main provisions concerning the strong moment problem. More precisely, strong classical, when studying the possibility of representing a sequence of real numbers . in the integral form for all integers moments.

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Applications of the Spectral Theory of Jacobi Matrices and Their Generalizations to the IntegrationIn this chapter, the difference analogue of the well-known procedure for finding solutions of the Cauchy problem for some nonlinear partial differential equations, in particular the Korteweg-de-Vries (KdV) equation, is presented, using the inverse spectral problem for the Sturm-Liouville equation on the half-axis.

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Yurij M. Berezansky,Mykola E. DudkinPresents direct and inverse problems for various classes of Jacobi type matrices.Uses different approaches and novel methods.Develops the theory of block Jacobi matrices and their applications to mome

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Operator Theory: Advances and Applicationshttp://image.papertrans.cn/j/image/500126.jpg

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Unitary Block Jacobi Type Matrices and the Trigonometric Moment Problem, also has a block tri-diagonal structure and generates a unitary operator that acts in the . space like the space of sequences summable with a square. By using this connection, the existence of a one-to-one correspondence between probability measures on the unit circle and the block tri-diagonal Jacobi type unitary matrices is established.

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Block Jacobi Type Matrices and the Complex Moment Problem in the Exponential Form,em generates a unitary and the second one generates a self-adjoint operator in the space like the space of square summable sequences .-type space. A one-to-one correspondence is also established between probability measures on a compact set of the complex plane and such couple of matrices.

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