Abstract
Using W. Rudin’s method it is shown that the tauberian theorem can be generalized to several kernels other than the Poisson kernel. We also proof an inverse of the tauberian theorem, that is, an abelian theorem.References
Gehring, F. W. (1960) “Harmonic functions and tauberian theorems”, London Math. Soc. 10(3): 88–166.
Gehring, F. W. (1957) “The Fatou theorem and its converse”, Bull. Amer. Math. Soc. 85: 106–121.
De Guzmán, M. (1975) “Differentiation of integrals in IRn”, Lecture Notes in Mathematics 481, Springer–Verlag.
Hewitt, E.; Ross, K. A. (1963 y 1970) Abstract Harmonic Analysis, vols. I y II, Springer–Verlag.
Loomis, L. H. (1953) An Introduction to Abstract Harmonic Analysis, Van Nostrand.
Loomis, L. H.; Widdner, D. V. (1942) “The Poisson integral representation of functions which are positive and harmonic in a half plane”, Duke Math. Journal 9: 643–645.
Rudin, W. (1979) “Tauberian theorems for positive harmonic functions”, Bull. Amer. Math. Soc.
Wiener, N. (1932) “Tauberian theorems”, Ann. of Math. 33(2): 1–100, 787.
Comments
![Creative Commons License](http://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Copyright (c) 1995 Marielos Mora