Skip to main content
Log in

The problem of completing partial matrix functions as a classical interpolation problem

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. N. I. Akhiezer, The Classical Moments Problem [in Russian], Moscow (1961).

  2. M. S. Livshits, “On one application of the theory of Hermitian operators to the generalized moments problem,” Dokl. Akad. Nauk SSSR,44, No. 1, 3–7 (1944).

    MATH  MathSciNet  Google Scholar 

  3. Z. Nehari, “On bounded bilinear forms,” Ann. of Math.,65, No. 1, 153–162 (1957).

    MATH  MathSciNet  Google Scholar 

  4. V. M. Adamyan, D. Z. Arov, and M. G. Krein, “On infinite Hankel matrices and the generalized Caratheodory—Feyer and Riesz problems,” Funktsion. Analiz i ego Prilozh.,2, No. 1, 1–19 (1968).

    Google Scholar 

  5. V. M. Adamyan, D. Z. Arov, and M. G. Krein, “Infinite Hankel matrices and the generalized Caratheodory—Feyer and Schur problems,” Funktsion. Analiz i ego Prilozh.,2, No. 4, 1–17 (1968).

    Google Scholar 

  6. V. M. Adamyan, D. Z. Arov, and M. G. Krein, “Analytic properties of Schmidt pairs of Hankel operators and the generalized Schur—Takagi problem,” Mat. Sb.,86, No. 1, 34–75 (1971).

    MathSciNet  Google Scholar 

  7. V. M. Adamyan, D. Z. Arov, and M. G. Krein, “Infinite block Hankel matrices and the continuation problems associated with them,” Izv. Akad. Nauk Arm. SSR,6, Nos. 2-3, 87–112 (1971).

    Google Scholar 

  8. J. W. Helton, Operator Theory, Analytic Functions, Matrices, and Electrical Engineering, Am. Math. Soc., Providence.

  9. B. A. Francis and J. C. Doyle, “Linear control theory with H optimality criterion,” SIAM Journ. Contr. Optim.,25, No. 4, 815–844 (1987).

    MathSciNet  Google Scholar 

  10. B. A. Francis, “A guide to H-control theory,” in: Proc. NATO Adv. Res. Workshop, Groningen, Dec. 1–5, 1986.

  11. V. É. Katsnel'son, “Integral representations of Hermitian positive kernels of mixed type and the generalized Nehari problem. 1,” Teoriya Funktsii, Funktsion. Analiz i Ikh Prilozh.,43, 54–70 (1985).

    MATH  Google Scholar 

  12. R. Aroena and M. Cotlar, “Generalized Toeplitz kernels and Adamjan-Arov-Krein moment problems,” in: Toeplitz Centennial Operator Theory, Advances, and Applications,4, Birkhäuser, 1982, pp. 37–55.

  13. B. Fritzsche and B. Kirstein, “On generalized Nehary Problem,” Math. Nachr.138, 217–237 (1988).

    MathSciNet  Google Scholar 

Download references

Authors

Additional information

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 56, pp. 105–122, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Katsnelson, V.É. The problem of completing partial matrix functions as a classical interpolation problem. J Math Sci 76, 2525–2537 (1995). https://doi.org/10.1007/BF02364910

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02364910

Keywords

Navigation