Skip to main content
SpringerLink
Log in

Miscellaneous problems

  • Chapter
  • First Online:
Linear and Complex Analysis Problem Book 3

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1574))

  • 901 Accesses

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Aizerman M. A., Gantmaher F. R., Absolute Stability of Control Systems, Ac. Sci. USSR, Moscow, 1963. (Russian)

    Google Scholar 

  2. Yakubovich V. A., The S-procedure in nonlinear control theory, Vestnik Leningrad Univ., Math. 1 (1971), 62–77 (Russian); English transl. in Vestnik Leningrad Univ., Math. 4 (1977), 73–93.

    MathSciNet  MATH  Google Scholar 

  3. Yakubovich V. A., Minimization of quadratic functionals under the quadratic constraints and the necessity of a frequency condition in the quadratic criterion for absolute stability of nonlinear control systems, Dokl. Akad. Nauk SSSR 209 (1973), 1039–1042 (Russian); English transl. in Soviet Math. Dokl. 14 (1973), 593–597.

    MathSciNet  MATH  Google Scholar 

  4. Gelig A. Ch., Leonov G. A., Yakubovich V. A., The Stability of Nonlinear Systems with a Nonunique Equilibrium State, Nauka, Moscow, 1978. (Russian)

    MATH  Google Scholar 

  5. Fradkov A. L., Yakubovich V. A., S-procedure and the duality relation in nonconvex problems of quadratic programming, Vestnik Leningrad Univ., Math. 1 (1973), 81–87 (Russian); English transl. in Vestnik Leningrad Univ., Math. 6 (1978).

    MATH  Google Scholar 

  6. Yakubovich V. A., One method for solving special global optimization problems, Vestnik Leningrad Univ., Math., I. 2 (1992), no. 8, 58–62. (Russian)

    MathSciNet  Google Scholar 

  7. Dines L. L., On the mapping of n quadratic forms, Bull. Am. Math. Soc. 48 (1942), no. 6, 467–471.

    Article  MathSciNet  MATH  Google Scholar 

  8. Fan Ming, Two problems on an n-tuple of operators, Uppsala University Department of Mathematics, February 1990, Report 1990:2.

    Google Scholar 

  9. Abramov Ju. Sh., Variation Methods in Operator Pencils Theory, Leningrad University, 1983. (Russian)

    Google Scholar 

  10. Dash A. T., Joint numerical range, Glasnik Matematički, ser. III 7(27) (1972), 75–81.

    MathSciNet  MATH  Google Scholar 

  11. Megretsky A., Treil S., S-procedure and power distribution inequalities: a new method in optimization and robustness of uncertain systems, Preprint of Mittag-Leffler Institute 1 (1990/91).

    Google Scholar 

  12. Shor N. Z., Stecenco S. I., Quadratic Extremal Problems and Nondifferentiable Optimization, Naukova Dumka, Kiev, 1989. (Russian)

    Google Scholar 

  13. Vershik A. M., Quadratic forms positive on the cone and quadratic duality, In: Automorphic functions and number theory II, Zap. Nauch. Semin. LOMI 134 (1984), 59–83. (Russian)

    Google Scholar 

Reference

  1. Ashmanov S. A., Introduction to mathematical economics, Nauka, Moscow, 1984. (Russian)

    MATH  Google Scholar 

References

  1. Azizov T. Ya., Iokhvidov I. S., Linear Operators in Spaces with Indefinite Metric, John Wiley and Sons, Chichester-New-York-Brisbane-Toronto-Singapore, 1989.

    MATH  Google Scholar 

  2. Bognar J., Indefinite Inner Product Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 78, Springer-Verlag, Berlin-Heidelberg-New-York, 1974.

    Book  MATH  Google Scholar 

  3. Iokhvidov I. S., Krein M. G., Spectral theory of operators in spaces with an indefinite metric, II, Amer. Math. Soc. Translations 34, no. 2, 283–373.

    Google Scholar 

References

  1. Akhiezer N. I., Lectures on Approximation Theory, “Nauka”, Moscow, 1965. (Russian)

    MATH  Google Scholar 

  2. Gorin E. A., Bernstein inequalities from the perspective of operator theory, Vestnik Kharkov. Gos. Un-ta. Ser. Mekh.-Matem., vyp. 45 205 (1980), 77–105. (Russian)

    MathSciNet  Google Scholar 

  3. Gorin E. A., Norvidas S. T., Extremals of some differential operators, School on theory of operators on functional spaces, Abstracts of lectures, Minsk, July 4–11, 1982, pp. 48–49. (Russian)

    Google Scholar 

  4. Zygmund A., Trigonometric Series, vol. 1, Cambr. Univ. Press, 1959.

    Google Scholar 

  5. Lukacs E., Characteristic Functions, 2-nd ed., Griffin, London, 1970.

    MATH  Google Scholar 

References

  1. Brudny Yu. A., Gorin E. A., Isometric representations and differential inequalities, Izd. Yarosl. Univ., Yaroslavl’, 1981, pp. 1–92. (Russian)

    Google Scholar 

  2. Norvidas S. T., On stability of differential operators in spaces of entire functions, Dokl. AN SSSR 291 (1986), no. 3, 548–552. (Russian)

    MathSciNet  MATH  Google Scholar 

  3. Norvidas S. T., On differential inequalities in Banach spaces of entire functions, Litovskii Mat. Zh. 30, no. 2, 345–358. (Russian)

    Google Scholar 

References

  1. Arnold V. I., Certain topological invariants of algebraic functions, Trudy Moskov. Mat. Obsc. 21 (1970), 27–46. (Russian)

    MathSciNet  Google Scholar 

  2. Gorin E. A., Lin V. Ya., Algebraic equations with continuous coefficients and some problems of the algebraic theory of braids, Mat. Sb. 78 (120) (1969), no. 4, 579–610 (Russian); English transl. in Math. USSR Sbornik 7 (1969), no. 4, 569–596.

    MathSciNet  Google Scholar 

  3. Fuks D. B., Cohomologies of the braid group mod 2, Funkts. Anal. i Prilozh. 4 (1970), no. 2, 62–73 (Russian); English transl. in Funct. Anal. and Appl. 4 (1970), no. 2, 143–151.

    MathSciNet  MATH  Google Scholar 

  4. Vainshtein F. V., Cohomologies of braid groups, Funkts. Anal. i Prilozh. 12 (1978), no. 2, 72–74 (Russian); English transl. in Funct. Anal. and Appl. 12 (1978), no. 2, 135–137.

    MathSciNet  Google Scholar 

  5. Lin V. Ya., Algebroid functions and holomorphic elements of homotopy groups of a complex manifold, Doklady Akad. Nauk SSSR 201 (1971), no. 1, 28–31 (Russian); English transl. in Soviet Math. Dokl. 12 (1971), no. 6, 1608–1612.

    MathSciNet  Google Scholar 

  6. Lin V. Ya., Algebraic functions with universal discriminant manifolds, Funkts. Anal. i Prilozh. 6 (1972), no. 1, 81–82 (Russian); English transl. in Funct. Anal. and Appl. 6 (1972), no. 1, 73–75.

    Google Scholar 

  7. Lin V. Ya, On superpositions of algebraic functions, Funkts. Anal. i Prilozh. 6 (1972), no. 3, 77–78 (Russian); English transl. in Funct. Anal. and Appl. 6 (1972), no. 3, 240–241.

    MathSciNet  Google Scholar 

  8. Kaliman Sh. I., A holomorphic universal covering of the space of polynomials without multiple roots, Funkts. Anal. i Prilozh. 9 (1975), no. 1, 71 (Russian); English transl. in Funct. Anal. and Appl. 9 (1975), no. 1, 67–68.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kaliman Sh. I., A holomorphic universal covering of the space of polynomials without multiple roots, Teor. Funktsii Funkts. Anal. i Prilozh. Vyp. 28, Kharkov, 1977, pp. 25–35. (Russian)

    MathSciNet  MATH  Google Scholar 

  10. Kaliman Sh. I., Holomorphic endomorphisms of the variety of complex polynomials with determinant 1, Uspekhi Mat. Nauk 31 (1976), no. 1, 251–252. (Russian)

    MathSciNet  Google Scholar 

  11. Lin V. Ya., Representations of the braid group by permutations, Uspekhi Mat. Nauk 27 (1972), no. 3, 192 (Russian)

    Google Scholar 

  12. Lin V. Ya., Representations of braids by permutations, Uspekhi Mat. Nauk 29 (1974), no. 1, 173–174. (Russian)

    Google Scholar 

  13. Lin V. Ya., Superpositions of algebraic functions, Funkts. Anal. i Prilozh. 10 (1976), no. 1, 37–45 (Russian); English transl. in Funct. Anal. and Appl. 10 (1976), no. 1, 32–38.

    MathSciNet  MATH  Google Scholar 

  14. Bandman T. N., Holomorphic functions omitting two values on an affine surface, Vestnik Moskov. Univ. Ser. I, Matem., Mekh. (1980), no. 4, 43–45. (Russian)

    MathSciNet  MATH  Google Scholar 

  15. Lin V. Ya., Artin braids and related groups and spaces, Itogi Nauki i Tekhniki., Algebra. Topology. Geometry. Vol. 17, Akad. Nauk SSSR, VINITI, Moscow, pp. 159–227. (Russian)

    Google Scholar 

Reference

  1. Lin V. Ya., Zaidenberg M. G., Doklady Akad. Nauk SSSR 271 (1983), no. 5, 1048–1052. (Russian)

    MathSciNet  Google Scholar 

References

  1. Badkov B. M., Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval, Matem. Sborn. 95 (1974), no. 2, 229–262. (Russian)

    MathSciNet  Google Scholar 

  2. Gulisashvili A. B., Singularities of summable functions, Zapiski nauchn. sem. LOMI 113 (1981), 76–96 (Russian); English transl. in J. Soviet Math. 22 (1983), no. 6, 1743–1757.

    MathSciNet  MATH  Google Scholar 

  3. Gulisashvili A. B., Rearrangements, arrangements of signs, and convergence of sequences of operators, Zapiski nauchn. sem. LOMI 107 (1981), 46–70 (Russian); English transl. in J. Soviet Math. 36 (1987), no. 3, 326–341.

    MathSciNet  MATH  Google Scholar 

  4. Tsereteli O. D., Conjugate functions, Matem. Zametki 22 (1977), no. 5, 771–783. (Russian)

    Google Scholar 

  5. Tsereteli O. D., Conjugate functions, Doctoral dissertation, Tbilisi, 1976. (Russian)

    Google Scholar 

  6. Tsereteli O. D., A certain case of summability of conjugate functions, Trudy Tbilisskogo Matem. Inst. AN Gruz. SSR 34 (1968), 156–159 (Russian)

    MathSciNet  Google Scholar 

Download references

Authors
  1. Victor P. Havin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolai K. Nikolski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Victor P. Havin Nikolai K. Nikolski

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this chapter

Cite this chapter

Havin, V.P., Nikolski, N.K. (1994). Miscellaneous problems. In: Havin, V.P., Nikolski, N.K. (eds) Linear and Complex Analysis Problem Book 3. Lecture Notes in Mathematics, vol 1574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101070

Download citation

  • DOI: https://doi.org/10.1007/BFb0101070

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57871-0

  • Online ISBN: 978-3-540-48368-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation