Skip to main content
SpringerLink
Log in

Spectral representation for generalized operator-valued Toeplitz kernels

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We prove an integral representation for operator-valued Toeplitz kernels. The proof is based on the spectral theory of the corresponding differential operator constructed from this kernel and acting in a Hilbert space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Cotlar and C. Sadosky, “On the Helson-Szegä theorem and related class of modified Toeplitz kernels,” in: Proceedings of the Symposium on Pure Mathematics, 35, Part 1 (1979) pp. 383–407.

    MathSciNet  Google Scholar 

  2. R. Bruzual, “Local semigroups of contractions and some applications to Fourier representation theorems,” Integr. Equat. Operator Theory, 10, 780–801 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  3. M. B. Bekker, “On one integral representation of Hermitian-positive matrix kernels of special structure,” Ukr. Mat. Zh., 40, No. 5, 626–628 (1988).

    MATH  MathSciNet  Google Scholar 

  4. M. Bekker, “On the extension problem for continuous positive definite generalized Toeplitz kernels defined on a finite interval,” Integr. Equat. Operator Theory, 34, No. 4, 379–397 (1999).

    Article  MathSciNet  Google Scholar 

  5. Yu. M. Berezans’kyi, “Generalization of the Bochner theorem to expansions in eigenfunctions of partial differential equations,” Dokl. Akad. Nauk SSSR, 110, No. 6, 893–896 (1956).

    MathSciNet  Google Scholar 

  6. Yu. M. Berezans’kyi, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

    Google Scholar 

  7. Yu. M. Berezans’kyi and O. B. Chernobai, “On the theory of generalized Toeplitz kernels,” Ukr. Mat. Zh., 52, No. 11, 1458–1472 (2000).

    Google Scholar 

  8. O. B. Chernobai, “On the spectral theory of generalized Toeplitz kernels,” Ukr. Mat. Zh., 55, No. 6, 850–857 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  9. M. L. Gorbachuk, “On representation of positive-definite operator functions,” Ukr. Mat. Zh., 17, No. 2, 29–46 (1965).

    MATH  Google Scholar 

  10. M. L. Gorbachuk and V. I. Gorbachuk, Boundary-Value Problems for Differential Operator Equations [in Russian], Naukova Dumka, Kiev (1964).

    Google Scholar 

  11. Yu. M. Berezans’kyi, G. F. Us, and Z. G. Sheftel’, Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1999).

    Google Scholar 

  12. Yu. M. Berezans’kyi, “Some generalizations of the classical moment problem,” Integr. Equat. Operator Theory, 44, No. 3, 255–289 (2002).

    Article  Google Scholar 

  13. Yu. M. Berezans’kyi and V. A. Tesko, “Spaces of test and generalized functions related to generalized translation operators,” Ukr. Mat. Zh., 55, No. 12, 1587–1657 (2003).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ukrainian State Tax Academy, Irpin’

    O. B. Chernobai

Authors
  1. O. B. Chernobai
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1698–1710, December, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chernobai, O.B. Spectral representation for generalized operator-valued Toeplitz kernels. Ukr Math J 57, 1995–2010 (2005). https://doi.org/10.1007/s11253-006-0044-2

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0044-2

Keywords

Search

Navigation