References
R. Bellman, A note on periodic functions and their derivatives, Journal London Math. Soc.18, 1943, 140–142.
L. Collatz, Konvergenzbeweis und Fehlerabschätzung für das Differenzenverfahren bei Eigenwertproblemen gewöhnlicher Differentialgleichungen zweiter und vierter Ordnung, Deutsche Math.2, 1937, 189–215.
L. Collatz, Eigenwertprobleme und ihre numerische Behandlung (Leipzig, 1945. Akad. Verlag).
R. Courant andD. Hilbert, Methods of mathematical physics, I (New York, 1953).
G. E. Forsythe, Asymptotic lower bounds for the frequencies of certain polygonal membranes, Pacific J. Math.4, 1954, 467–480.
G. E. Forsythe, Asymptotic lower bounds for the fundamental frequency of convex membranes, Pacific J. Math., to appear.
H. Frazer, Note onHilbert's inequality, Journal London Math. Soc.21, 1946, 7–9.
G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities (Cambridge, England {1}, 1934, {2}, 1952).
D. G. Northcott, Some inequalities between periodic functions and their derivatives, Journal London Math. Soc.14, 1939, 198–202.
A. M. Ostrowski, Über die Absolutabweichung einer differentierbaren Funktion von ihrem Integralmittelwert, Comm. Mat. Helvetici,10, 1937–8, 226–227.
G. Pólya andG. Szegö, Isoperimetric inequalities in mathematical physics. Annals of Math. Studies27, 1951, (Princeton Univ. Press, Princeton, USA).
D. E. Rutherford, Some continuant determinants arising in physics and chemistry, I, Proc. Royal Soc. Edinburgh.62A, 1947, 229–236.
D. E. Rutherford, Some continuant determinants arising in physics and chemistry, II, Proc. Royal Soc. Edinburgh,63A, 1952, 232–241.
John Todd, The condition of certain matrices, II, Archiv d. Math.5, 1954, 249–257.
J. Williamson, The latent roots of a matrix of special type, Bulletin American Math. Soc.37, 1931, 585–590.
W. Blaschke, Kreis und Kugel (Leipzig 1916, New York, 1949).
H. Bückner, Über Konvergenzsätze, die sich bei der Anwendung eines Differenzenverfahrens auf ein Sturm-Liouvillesches Eigenwertproblem ergeben, Math. Zeit.51, 1948, 423–465.
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01302991