Skip to main content
SpringerLink
Log in

Inversion of Finite Toeplitz Matrices

  • Chapter
Convolution Equations and Singular Integral Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 206))

  • 880 Accesses

Abstract

In this communication Toeplitz matrices of the form ∥a j-k ∥ n j,k=0 , where a j (j=0,±1,...,±n are elements of some noncommutative algebra, and their continual analogues are considered. The theorems presented here are generalizations of theorems from [1] to the noncommutative case.

The paper was originally published as И.Ц. Гохбсрг. Г. Хайниг, Об обращцнии концчных тэблицовых Матрис, Матом. Исслод 8 (1973), No 3(29), 151–156. MR0341163 (49 #5913), Zbl 0337.15004.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. I.C. Gohberg and A.A. Semencul, The inversion of finite Toeplitz matrices and their continual analogues. Matem. Issled. 7 (1972), no. 2(24), 201–223 (in Russian). MR0353038 (50 #5524), Zbl 0288.15004.

    MATH  MathSciNet  Google Scholar 

  2. I.C. Gohberg and N.Ya. Krupnik, A formula for the inversion of finite Toeplitz matrices. Matem. Issled. 7 (1972), no. 2(24), 272–283 (in Russian). MR0353039 (50 #5525), Zbl 0288.15005.

    MathSciNet  Google Scholar 

  3. L.M. Kutikov, The structure of matrices which are the inverse of the correlation matrices of random vector processes. Zh. Vychisl. Matem. Matem. Fiz. 7 (1967), 764–773 (in Russian). English translation: U.S.S.R. Comput. Math. Math. Phys. 7 (1967), no. 4, 58–71. MR0217863 (36 #952), Zbl 0251.15023.

    MathSciNet  Google Scholar 

  4. I.I. Hirschman, Jr., Matrix-valued Toeplitz operators. Duke Math. J. 34 (1967), 403–415. MR0220002 (36 #3071), Zbl 0182.46203.

    Article  MATH  MathSciNet  Google Scholar 

  5. L.M. Kutikov, Inversion of correlation matrices. Izv. Akad. Nauk SSSR Tehn. Kibernet. (1965), no. 5, 42–47 (in Russian). English translation: Engineering Cybernetics (1965), no. 5, 35–39. MR0203871 (34 #3718).

    Google Scholar 

Download references

Authors
  1. Israel Gohberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georg Heinig
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Leonid Lerer

  2. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  3. Department of Mathematics, College of William & Mary, Williamsburg, VA, 23187-8795, USA

    Ilya M. Spitkovsky

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Basel AG

About this chapter

Cite this chapter

Gohberg, I., Heinig, G. (2010). Inversion of Finite Toeplitz Matrices. In: Lerer, L., Olshevsky, V., Spitkovsky, I.M. (eds) Convolution Equations and Singular Integral Operators. Operator Theory: Advances and Applications, vol 206. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8956-7_2

Download citation

Publish with us

Policies and ethics

Search

Navigation