Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Toeplitz Matrices and Operators
  4. Content listing

Refine listing

Refine listing

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

21 results in Toeplitz Matrices and Operators

Page 1 of 2

  • 5 - Toeplitz Matrices: Moments, Spectra, Asymptotics

  • Nikolaï Nikolski, Université de Bordeaux
  • Translated by Danièle Gibbons, Greg Gibbons
  • Book:
    Toeplitz Matrices and Operators
    Published online:
    06 December 2019
    Print publication:
    02 January 2020, pp 230-328

  • Summary

    Trigonometric moment problem, positive definite Toeplitz matrices, orthogonal polynomials.

    Arveson’s distance formula, the four-block lemma, Julia’s lemma.

    Inversion of a Toeplitz matrix by Gohberg-Sementsul and Baxter-Hirschman, inversion by the finite section method.

    Circulants.

    Toeplitz determinants and their asymptotics, equidistribution following Weyl, asymptotic distribution of Toeplitz spectra (following Szegő) and of circulants.

    The “strong Szegő theorem,” Krein-Dirichlet algebra.

    The Helton-Howe and Berger-Shaw formulas of det/trace.

    Positive harmonic functions, holomorphic functions of the Schur class

    Inversion of Wiener–Hopf operators by the finite section method, case of a rational symbol.

    Cauchy and Hilbert determinants, Libkind-Widom and Borodin Okounkov formulas.

  • 1 - Why Toeplitz–Hankel? Motivations and Panorama

  • Nikolaï Nikolski, Université de Bordeaux
  • Translated by Danièle Gibbons, Greg Gibbons
  • Book:
    Toeplitz Matrices and Operators
    Published online:
    06 December 2019
    Print publication:
    02 January 2020, pp 1-30

  • Summary

    Four cornerstones of the theory of Toeplitz operators: the Riemann–Hilbert problem (RHP), the singular integral operators (SIO), the Wiener–Hopf operators (WHO), and last (but not least) the Toeplitz matrices and operators (TMO) (strictly speaking, compressions of multiplication operators).

    The founding contributions of Bernhard Riemann, David Hilbert, George Birkhoff, Otto Toeplitz, Gábor Szegő, Norbert Wiener, and Eberhard Hopf.

    The modern and post-modern periods of the theory.

  • 3 - H2 Theory of Toeplitz Operators

  • Nikolaï Nikolski, Université de Bordeaux
  • Translated by Danièle Gibbons, Greg Gibbons
  • Book:
    Toeplitz Matrices and Operators
    Published online:
    06 December 2019
    Print publication:
    02 January 2020, pp 101-177

  • Summary

    The Toeplitz algebra, semi-commutators and symbolic calculus, index and Cauchy topological index, homotopy of symbols.

    dist(f, H∞) and dist(f, H∞ + C), local principle, local distances.

    The spectrum and essential spectrum of Toeplitz operators, sectorial and locally sectorial symbols, spectral inclusions.

    Wiener–Hopf factorization.

    Self-adjoint Toeplitz operators, Hankel operators in the Toeplitz algebra.

Page 1 of 2