Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-20T00:25:15.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-measurable interpolation sets

II. functions regular in an angle

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 an earlier paper the problem of the interpolation of an integral function f(z) in terms of the values taken on a sequence zn was studied by means of generalized σ-functions with zeros at zn. The purpose of the present paper is to show that the methods used in I can be modified to deal with functions of finite order and type in the angle Sα, | arg z | ≤ α. There is even a considerable saving since, for an Sα with α < π, we can escape from the awkward convergence condition Dρ (ii) of I. Most of our results, and to a great extent also their proofs, are direct generalizations of well-known results for the lattice points m + in (cf. the references at the end of I, particularly (2), (5), (6), (14), (18)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 733 - 740
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

† Noble, M. E., ‘Non-measurable interpolation sets, I, Integral functions’, Proc. Cambridge Phil. Soc. 47 (1951), 713CrossRefGoogle Scholar, referred to in future as I.

* Cartwright, M. L., Quart. J. Math. (Oxford), 7 (1936), 44–55.Google Scholar

† Ganapathy, V. Iyer, Quart. J. Math. (Oxford), 9 (1938), 206.Google Scholar

* Cf., for example, Valiron, G., Integral functions (Toulouse, 1923), p. 53.Google Scholar

† Bernstein, V., Ann. Mat. (4), 12 (1934), 173–96CrossRefGoogle Scholar, Lemma II.

* Ganapathy, V. Iyer, Quart. J. Math. (Oxford), 9 (1938), 206–15.Google Scholar

* Cf. Pflüger, A., Proc. London Math. Soc. (2), 42 (1937), 367–72.Google Scholar