Skip to main content
Log in

Discrete analogs of inequalities of Wirtinger

  • Published:
Monatshefte für Mathematik 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. R. Bellman, A note on periodic functions and their derivatives, Journal London Math. Soc.18, 1943, 140–142.

    Google Scholar 

  2. L. Collatz, Konvergenzbeweis und Fehlerabschätzung für das Differenzenverfahren bei Eigenwertproblemen gewöhnlicher Differentialgleichungen zweiter und vierter Ordnung, Deutsche Math.2, 1937, 189–215.

    Google Scholar 

  3. L. Collatz, Eigenwertprobleme und ihre numerische Behandlung (Leipzig, 1945. Akad. Verlag).

  4. R. Courant andD. Hilbert, Methods of mathematical physics, I (New York, 1953).

  5. G. E. Forsythe, Asymptotic lower bounds for the frequencies of certain polygonal membranes, Pacific J. Math.4, 1954, 467–480.

    Google Scholar 

  6. G. E. Forsythe, Asymptotic lower bounds for the fundamental frequency of convex membranes, Pacific J. Math., to appear.

  7. H. Frazer, Note onHilbert's inequality, Journal London Math. Soc.21, 1946, 7–9.

    Google Scholar 

  8. G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities (Cambridge, England {1}, 1934, {2}, 1952).

  9. D. G. Northcott, Some inequalities between periodic functions and their derivatives, Journal London Math. Soc.14, 1939, 198–202.

    Google Scholar 

  10. A. M. Ostrowski, Über die Absolutabweichung einer differentierbaren Funktion von ihrem Integralmittelwert, Comm. Mat. Helvetici,10, 1937–8, 226–227.

    Google Scholar 

  11. G. Pólya andG. Szegö, Isoperimetric inequalities in mathematical physics. Annals of Math. Studies27, 1951, (Princeton Univ. Press, Princeton, USA).

    Google Scholar 

  12. D. E. Rutherford, Some continuant determinants arising in physics and chemistry, I, Proc. Royal Soc. Edinburgh.62A, 1947, 229–236.

    Google Scholar 

  13. D. E. Rutherford, Some continuant determinants arising in physics and chemistry, II, Proc. Royal Soc. Edinburgh,63A, 1952, 232–241.

    Google Scholar 

  14. John Todd, The condition of certain matrices, II, Archiv d. Math.5, 1954, 249–257.

    Google Scholar 

  15. J. Williamson, The latent roots of a matrix of special type, Bulletin American Math. Soc.37, 1931, 585–590.

    Google Scholar 

  16. W. Blaschke, Kreis und Kugel (Leipzig 1916, New York, 1949).

  17. H. Bückner, Über Konvergenzsätze, die sich bei der Anwendung eines Differenzenverfahrens auf ein Sturm-Liouvillesches Eigenwertproblem ergeben, Math. Zeit.51, 1948, 423–465.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was partially supported by the United States Air Force, through the Office of Scientific Research of the Air Research and Development Command. It was performed in part under a contract between the American University and the National Bureau of Standards.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fan, K., Taussky, O. & Todd, J. Discrete analogs of inequalities of Wirtinger. Monatshefte für Mathematik 59, 73–90 (1955). https://doi.org/10.1007/BF01302991

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01302991

Keywords

Navigation