Have a personal or library account? Click to login
Volterra operator norms : a brief survey Cover
By: Thomas Ransford  
Open Access
|Jun 2023

References

  1. Allan, G. R., Power-bounded elements and radical Banach algebras. Linear operators (Warsaw, 1994), 38, 9–16,Polish Acad. Sci. Inst. Math., Warsaw, 1997.
  2. Böttcher, A. and Dörfler, P., On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line. Linear Algebra Appl.Vol 430, N 4,1057–1069,2009.
  3. Böttcher, A. and Dörfler, P., Weighted Markov-type inequalities, norms of Volterra operators, and zeros of Bessel functions.Math. Nachr. Vol. 283, No. 1,40–57, 2010.
  4. Böttcher, A. and Widom, H., On the eigenvalues of certain canonical higher-order ordinary differential operators. J. Math. Anal. Appl. Vol. 322, No. 2, 990–1000, 2006.
  5. Crouzeix, M., Bounds for analytical functions of matrices. Integral Equations Operator Theory. Vol. 48, No. 4, 461–477, 2004.
  6. Crouzeix, M. and Palencia, C., The numerical range is a(1+2) a\left( {1 + \sqrt 2 } \right) -spectral set. SIAM J. Matrix Anal. Appl. Vol. 38,No. 2, 649–655, 2017.
  7. Franco, Z. M. and Kaper, H. G. and Kwong, M. K. and Zettl, A., Best constants in norm inequalities for derivatives on ahalf-line. Proc. Roy. Soc. Edinburgh Sect. A. Vol. 100, No. 1-2, 67–84, 1985.
  8. Halmos, P. R., A Hilbert space problem book. Encyclopedia of Mathematics and its Applications. Vol. 17, Edition Second, 1982.
  9. Horgan, C. O., A note on a class of integral inequalities. Proc. Cambridge Philos. Soc.Vol. 74, 127–131, 1973.
  10. Kershaw, D., Operator norms of powers of the Volterra operator. J. Integral Equations Appl. Vol. 11, No. 3, 351–362, 1999.
  11. Khadkhuu, L. and Tsedenbayar, D., A note about Volterra operator. Math. Slovaca. Vol. 68, No. 5, 2018.
  12. Khadkhuu, L. and Tsedenbayar, D., On the numerical range and numerical radius of the Volterra operator. Izv. Irkutsk. Gos. Univ. Ser. Mat. Vol. 24, pp. 102–108, 2018.
  13. Lao, N. and Whitley, R., Norms of powers of the Volterra operator. Integral Equations Operator Theory. Vol. 27, No. 4, 419–425,1997.
  14. Little, G. and Reade, J. B., Estimates for the norm of the nth indefinite integral. Bull. London Math. Soc. Vol. 30, No. 5, 539–542, 1998.
  15. Lumer, G., Semi-inner-product spaces. Trans. Amer. Math. Soc. Vol. 100, 29–43, 1961.
  16. Lyubich, Y. and Tsedenbayar, D., The norms and singular numbers of polynomials of the classical Volterra operator in L2(0, 1). Studia Math. Vol. 199, No. 2, 171–184, 2010.
  17. Ransford, T. and Walsh, N., Norms of polynomials of the Volterra operator, J. Math. Anal. Appl. 517 (2023), paper no. 126626.
  18. Ter Elst, A. F. M. and Zem´anek, J., Contractive polynomials of the Volterra operator. Studia Math. Vol. 240, No. 3, 201–211, 2018.
  19. Thorpe, B., The norm of powers of the indefinite integral operator on (0, 1). Bull. London Math. Soc. Vol. 30, No. 5, 543–548, 1998.
Language: English
Page range: 276 - 290
Submitted on: Jul 29, 2022
Accepted on: Nov 26, 2022
Published on: Jun 7, 2023
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2023 Thomas Ransford, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.