Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T16:04:23.244Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-measurable interpolation sets

I. Integral functions

Published online by Cambridge University Press:  24 October 2008

M. E. Noble
M. E. Noble
Affiliation:
Queens' CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

In two classical papers (1, 2) J. M. Whittaker introduced the study of integral functions bounded at the lattice points m + in(m, n = 0, ± 1, …,). He succeeded in showing (cf. also G. Polya(3)) that an integral function of at most the minimum type of order 2 uniformly bounded at the lattice points was necessarily constant. This result was improved almost simultaneously by A. Pflüger(5) and V. Ganapathy Iyer(11), who showed that the result was true also for functions of type K<½12π of order 2. The example of Weierstrass's σ(z) function shows that theirs is a best possible result in this direction.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 713 - 732
Copyright
Copyright © Cambridge Philosophical Society 1951

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Whittaker, J. M.Proc. Edinburgh Math. Soc. (2), 2 (1930), 111–28.CrossRefGoogle Scholar
(2)Whittaker, J. M.Proc. London Math. Soc. (2), 37 (1934), 383–401.CrossRefGoogle Scholar
(3)Polya, G.Jber. Dtsch. Math. Ver. 43 (1933), 67.Google Scholar
(4)Polya, G.Math. Z. 29 (1928–1930), 549–640.CrossRefGoogle Scholar
(5)Pflüger, A.Proc. London Math. Soc. (2), 42 (1937), 305–15.CrossRefGoogle Scholar
(6)Pflüger, A.Compositio Math. 4 (1937), 367–72.Google Scholar
(7)Pflüger, A.Comment math. helvet. 11 (1938–1939), 180–213.CrossRefGoogle Scholar
(8)Pflüger, A.Comment math. helvet. 14 (1941–1942), 314–49.CrossRefGoogle Scholar
(9)Pflüger, A.Comment math. helvet. 18 (1945–1946), 177–203.CrossRefGoogle Scholar
(10)Lévine, B.Recueil Math. (Mat. Shornik), N.S., 8 (50) (1940), 437.Google Scholar
(11)Ganapathy, V. IyerJ. London Math. Soc. 11 (1936), 247–9.Google Scholar
(12)Ganapathy, V. IyerTrans. American Math. Soc. 42 (1937), 358–65.Google Scholar
(13)Ganapathy, V. IyerTrans. American Math. Soc. 43 (1938), 494.Google Scholar
(14)Ganapathy, V. IyerQuart. J. Math. (Oxford), 9 (1938), 206–15.Google Scholar
(15)Ganapathy, V. IyerMath. Z. 44 (1939), 195–200.CrossRefGoogle Scholar
(16)Maitland, B. J.Proc. London Math. Soc. (2), 45 (1939), 440–57.CrossRefGoogle Scholar
(17)Cartwright, M. L.Proc. London Math. Soc. (2), 43 (1937). 26–32.Google Scholar
(18)Cartwright, M. L.Quart. J. Math. (Oxford), 7 (1936), 46–55.Google Scholar
(19)Cartan, H.Ann. Sci. Éc. Norm. Sup. Paris, (3), 45 (1928), 255–346.CrossRefGoogle Scholar
(20)Milloux, H.J. Math. (9), 16 (1937), 179–198.Google Scholar
(21)Titchmarsh, E. C.Theory of functions (Oxford, 2nd ed. 1939).Google Scholar