The Classical Moment Problem as a Self-Adjoint Finite Difference Operator

  title={The Classical Moment Problem as a Self-Adjoint Finite Difference Operator},
  author={Barry Simon},
  journal={Advances in Mathematics},
  • B. Simon
  • Published 15 July 1998
  • Mathematics
  • Advances in Mathematics
Abstract This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Pade approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we obtain new results on the convergence of certain Pade approximants for series of Hamburger 

Second-Order Differential Operators in the Limit Circle Case

  • D. Yafaev
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2021
We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct

Self-adjoint Jacobi operators in the limit circle case

We consider symmetric Jacobi operators with recurrence coefficients such that the corresponding difference equation is in the limit circle case. Equivalently, this means that the associated moment

On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the

The Operator-Theoretic Approach to the Hamburger Moment Problem

In this chapter we begin the study of moment problems using self-adjoint operators and self-adjoint extensions on Hilbert spaces. The operator-theoretic approach is a powerful tool and it will be

On an application of the Boundary control method to classical moment problems.

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of

On the analytic form of the discrete Kramer sampling theorem

The classical Kramer sampling theorem is, in the subject of self-adjoint bound- ary value problems, one of the richest sources to obtain sampling expansions. It has be- come very fruitful in

The One-Dimensional Hamburger Moment Problem

In Chap. 16, we present a short and concise treatment of the one-dimensional Hamburger moment problem with an emphasis on the self-adjoint extension theory. Orthogonal polynomials and the Jacobi

A point interaction for the discrete Schrödinger operator and generalized Chebyshev polynomials

We consider semi-infinite Jacobi matrices corresponding to a point interaction for the discrete Schrodinger operator. Our goal is to find explicit expressions for the spectral measure, the resolvent,



m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices

We study inverse spectral analysis for finite and semi-infinite Jacobi matricesH. Our results include a new proof of the central result of the inverse theory (that the spectral measure determinesH).

Extremal spectral functions of a symmetric operator

Abstract : It is known that the finite dimensional extensions of a symmetric operator define extremal spectral functions of the operator. Finite dimensional extensions exist, however, only for

Theory of linear operators in Hilbert space

linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of the


In our first note, we introduced the terminology adapted to a study of linear transformations in complex Hilbert space and discussed certain geometrical aspects of self-adjoint transformations. We

The classical moment problem: Hilbertian proofs

More determinacy theory for the Livšic moments problem

Theq-Laguerre Polynomials and Related Moment Problems☆

Abstract We study two indeterminate Hamburger moment problems associated with q -Laguerre polynomials. The coefficients in their recurrence relations are of exponential growth. This completes earlier