Skip to main content
Log in

An estimate of the spectral radius of a certain singular integral operator

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

In this paper we find the spectral radius of a certain integral operator which is a generalization of the Cesàro operator.

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.

Similar content being viewed by others

References

  1. Vasil’ev, N. I., Klokov, Yu. A. Foundations of the Theory of Boundary Value Problems in Ordinary Differential Equations (Zinatne, Riga, 1978) [in Russian].

    Google Scholar 

  2. Parter, S. V., Stein, M. L., Stein, P. S. “On the Multiplicity of Solutions of a Differential Equation Arising in Chemical Reactor Theory,” Stud. Appl.Math. LIV, No. 4, 293–314 (1975).

    MathSciNet  Google Scholar 

  3. Williams, L. R., Leggett, R.W. “Multiple Fixed Point Theorems for Problems in Chemical Reactor Theory,” J.Math. Anal. and Appl., No. 69, 180–193 (1979).

    Google Scholar 

  4. Kiguradze, I. T., Shekhter, B. L. “Singular Boundary-Value Problems for Second Order Ordinary Differential Equations,” Itogi Nauki i Tekh., Ser. Sovrem. Probl. Mat. 30, 105–201 (1987).

    MathSciNet  Google Scholar 

  5. Azbelev, N. V., Maksimov, V. P., Rakhmatullina, L. F. Elements of the Contemporary Theory of Functional Differential Equations. Methods and Applications (Institute of Computer-Assisted Studies, Moscow, 2002) [in Russian].

    Google Scholar 

  6. Abdullaev, A. R. “On Solvability of the Cauchy Problem for Second Order Differential Equations in the Critical Case,” Trudy Instituta Prikladnoi Matematiki im. I. N. Vekua, No. 37, 5–12 (1990).

    Google Scholar 

  7. Azbelev, N. V., Alvesh, M. Zh., Bravyi, E. I. “On Singular Boundary Value Problems for a Second-Order Linear Functional-Differential Equation,” Russian Mathematics (Iz. VUZ) 43, No. 2, 1–9 (1999).

    MATH  MathSciNet  Google Scholar 

  8. Plaksina, I. M. “One Model Singular Problem,” Vestn. Permsk. Univ. Matem. Mekhan. Informatika, No. 1, 19–23 (2010) [in Russian].

    Google Scholar 

  9. Plaksina, I. M. “On Class of Singular Linear Functional-Differential Equations,” Russian Mathematics (Iz. VUZ) 56, No. 2, 80–83 (2012).

    MATH  MathSciNet  Google Scholar 

  10. Plaksina, I. M. “On Positiveness of the Cauchy Function of a Singular Linear Functional Differential Equation,” Russian Mathematics (Iz. VUZ) 57, No. 10, 13–18 (2013).

    MATH  MathSciNet  Google Scholar 

  11. Kungurtseva, A. V. “On a Class of Boundary Value Problems for Singular Equations,” Russian Mathematics (Iz. VUZ) 39, No. 12, 28–34 (1995).

    MATH  MathSciNet  Google Scholar 

  12. Plekhova, E. V. “On Solvability of the Cauchy Problem for a Singular Differential Equation,” Vestn. PGTU. Prikl. Matem. I Mekhan., No. 9, 177–182 (2011).

    Google Scholar 

  13. Abdullaev, A. R., Plekhova, E. V. “On the Spectrum of the Cesàro Operator,” Nauchno-Tekhnich. Vestn. Povolzh’ya, No. 4, 33–37 (2011).

    Google Scholar 

  14. Agarwal, R. P., O’Regan, D., Zernov, A. E. “A Singular Initial Value Problem for Some Functional Differential Equations,” J. Appl.Math. and Stochastic Anal., No. 3, 261–270 (2004).

    Google Scholar 

  15. Pelukh, G. P., Bel’skii, D. V. “Asymptotic Properties of Solutions to Functional-Differential Equations with Linearized Argument,” Neliniini Kolivannya 10, No. 1, 144–160 (2007).

    MathSciNet  Google Scholar 

  16. Hardy, G. H., Littlewood, J. E., Pólya, G. Inequalities (Cambridge University Press, 1934; GIIL, Moscow, 1948).

    Google Scholar 

  17. Muntean, I. “The Spectrum of the Cesàro Operator,” Mathematica. Revue d’analyse numerique et de theorie de l’approximation 22, No. 1, 97–105 (1980).

    MathSciNet  Google Scholar 

  18. Rhoades, B. E. “Norm and Spectral Properties of Some Weighted Mean Operators,” Mathematica. Revue d’analyse numerique et de theorie de l’approximation 26, No. 2, 143–152 (1984).

    MathSciNet  Google Scholar 

  19. Halmosh, P., Sander, V. Bounded Integral Operators on L 2 Spaces (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  20. Hutson, V., Pym, J., Applications of Functional Analysis and Operator Theory (Acad. Press, New York, 1980; Mir, Moscow, 1983).

    MATH  Google Scholar 

  21. Abdullaev, A. R., Plaksina, I. M. “On One Method for Estimating Norms of Singular Integral Operators,” Vestn. Permsk. Univ. Matem. Mekhan. Informatika, No. 2, 5–8 (2013).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. R. Abdullaev.

Additional information

Original Russian Text © A.R. Abdullaev, I.M. Plaksina, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 2, pp. 3–9.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdullaev, A.R., Plaksina, I.M. An estimate of the spectral radius of a certain singular integral operator. Russ Math. 59, 1–6 (2015). https://doi.org/10.3103/S1066369X15020012

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X15020012

Keywords

Navigation