Abstract
This paper is a comment on a paper by D.C. Russell “Tauberian-type results for convolutions of sequences” (cf. [9]). We wish to describe the relation between the results of Russell and the work of Essen on convolution inequalities (cf. [4], [5]).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Beurling, Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionnelle. Neuvième congrès des mathématiciens scandinaves, Helsingfors (1938), 345–366.
E.T. Copson, On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. (2) 17 (1970), 159–164.
H.G. Diamond and M. Essén, One-sided Tauberian theorems for kernels which change sign. Proc. of the London Math. Soc. (3) 36 (1978), 273–284.
M. Essén, Studies on a convolution inequality. Arkiv f. matematik 5 (1963), 113–152.
M. Essén, Note on “A theorem on the minimum modulus of entire functions” by Kjellberg. Math. Scand. 12 (1963), 12–14.
M. Essén, Banach algebra methods in renewal theory. Journal d’Analyse Math. 26 (1973), 303–336.
Y. Katznelson, An introduction to harmonic analysis. Wiley 1968.
D. C. Russell, On bounded sequences satisfying a linear inequality. Proc. of the Edinburgh Math. Soc. 19 (Series II, 1974), 11–16.
D. C. Russell, Tauberian-type results for convolution of sequences. In: W, Walter (ed)., General Inequalities 5, Birkhäuser Verlag, Basel, 1987, pp.103–113.
D. Widder, The Laplace transform. Princeton Univ. Press 1946.
N. Wiener and H.R. Pitt, On absolutely convergent Fourier Stieltjes transforms. Duke Math. J. 4 (1938), 420–436.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Essén, M. (1987). Tauberian Theorems, Convolutions and Some Results of D.C. Russell. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7192-1_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7194-5
Online ISBN: 978-3-0348-7192-1
eBook Packages: Springer Book Archive