Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T18:40:00.418Z Has data issue: false hasContentIssue false
  • English
  • Français

A Bessel function inequality connected with stability of least square smoothing, II

Published online by Cambridge University Press:  18 May 2009

Lee Lorch  and
Peter Szego
Lee Lorch
Affiliation:
Summer Research Institute(Canadian Mathematical Congress)University of AlbertaEdmonton, Canada
Peter Szego
Affiliation:
Ampex CorporationRedwood City, California, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In accordance with customary notation, Jv(t) denotes the Bessel function of the first kind and order v, jvk its kth positive zero and jv, 0 = 0.

The object of this note is to prove that

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 9 , Issue 2 , July 1968 , pp. 119 - 122
Copyright
Copyright © Glasgow Mathematical Journal Trust 1968

References

REFERENCES

1.Lorch, Lee and Szego, Peter, Higher monotonicity properties of certain Sturm-Liouville functions, Acta Math. 109 (1963), 55–73.Google Scholar
2.Lorch, Lee and Szego, Peter, Higher monotonicity properties of certain Sturm-Liouville functions II, Bull, de l'Acad. Polonaise des Sci. Sér. Math. Astr. et Phys. 11 (1963), 455–457.Google Scholar
3.Lorch, Lee and Szego, Peter, A Bessel function inequality connected with stability of least square smoothing, Proc. Amer. Math. Soc. 17 (1966), 330–332.CrossRefGoogle Scholar
4.Trench, William F., On the stability of midpoint smoothing with Legendre polynomials, Proc. Amer. Math. Soc. 18 (1967), 191–199.Google Scholar
5.Trench, William F., Bounds on the generating functions of certain smoothing operations, Proc. Amer. Math. Soc. 18 (1967), 200–206.Google Scholar
6.Watson, G. N., A treatise on the theory of Bessel functions, 2nd edition (Cambridge, 1944).Google Scholar
7.Wilf, Herbert S., The stability of smoothing by least squares, Proc. Amer. Math. Soc. 15 (1964), 933–937; Errata, ibid., 17 (1966) 542.CrossRefGoogle Scholar