caa a22 4500 386307229 CHVBK 20180307111533.0 cr unu---uuuuu 161130e198810 xx s 000 0 eng 10.1017/S144678870003010X doi S144678870003010X pii (NATIONALLICENCE)cambridge-10.1017/S144678870003010X Cohen Joel M. Department of Mathematics, University of Bari 70125 Bari, ItalyDepartment of Mathematics, University of Maryland College Park, Maryland 20742, U.S.A. Bounded spherical functions for abstract operators [Elektronische Daten] [Joel M. Cohen] The aim of this paper is to study the spherical functions associated to an operator. These functions can be thought of abstractly as being eigenfunctions of the operator which can be expressed in terms of the operator. The meaning of these properties will be made precise as will a notion of boundedness. The results are obtained by studying a specific shift operator on the algebra of functionals on the complex polynomial ring. For the class studied, we obtain ellipses of eigenvalues for which there exist bounded spherical functions. As an application of the results, we study radial functions on discrete groups. Copyright © Australian Mathematical Society 1988 primary 43 A 90 nationallicence secondary 42 C 10 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/2(1988-10), 195-203 1446-7887 45:2<195 1988 45 JAZ https://doi.org/10.1017/S144678870003010X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S144678870003010X text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cohen Joel M. Department of Mathematics, University of Bari 70125 Bari, ItalyDepartment of Mathematics, University of Maryland College Park, Maryland 20742, U.S.A NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/2(1988-10), 195-203 1446-7887 45:2<195 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge