The inverse spectral problem for self-adjoint Hankel operators

1995/01/01 by A. V. Megretskii, V. V. Peller, S. R. Treil +1 · 5 citations
Physics and Astronomy · Decision Sciences · Mathematics · #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #Numerical methods in inverse problems

paper · pdf · doi:10.1007/bf02392468

Abstract

In §8.5 we have considered a geometric problem in the theory of stationary Gaussian processes and we have reduced this problem to the problem of the description of the bounded linear operators on Hilbert space that are unitarily equivalent to moduli of Hankel operators. In this chapter we are going to solve the latter problem, which in turn will lead to a solution of the above geometric problem in prediction theory.

Cited by

• On regularity of compressions and diagonals of operator functions
• Ergodic Hankel operators
• An inverse problem for self-adjoint positive Hankel operators
• Hankel and Toeplitz operators: continuous and discrete representations
• Spectral asymptotics for compact self-adjoint Hankel operators

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• A Dynamical System Approach to the Inverse Spectral Problem for Hankel Operators: A Model Case
• A new representation of Hankel operators and its spectral consequences
• An inverse problem for self-adjoint positive Hankel operators