Compactly bounded convolutions of measures
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- by Adam W. Parr PDF
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Abstract:
In this paper we extend classical results concerning generalized convolution structures on measure spaces. Given a locally compact Hausdorff space $X$, we show that a compactly bounded convolution of point masses that is continuous in the topology of weak convergence with respect to $C_{c}(X)$ can be extended to a general convolution of measures which is separately continuous in the topology of weak convergence with respect to $C_{b}(X)$.References
- R. Creighton Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. MR 105611
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
- Robert I. Jewett, Spaces with an abstract convolution of measures, Advances in Math. 18 (1975), no. 1, 1–101. MR 394034, DOI 10.1016/0001-8708(75)90002-X
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
- A. Parr, Signed Hypergroups, Ph.D. Thesis, University of Oregon (1997).
- John S. Pym, Weakly separately continuous measure algebras, Math. Ann. 175 (1968), 207–219. MR 222665, DOI 10.1007/BF02052723
- Margit Rösler, Convolution algebras which are not necessarily positivity-preserving, Applications of hypergroups and related measure algebras (Seattle, WA, 1993) Contemp. Math., vol. 183, Amer. Math. Soc., Providence, RI, 1995, pp. 299–318. MR 1334785, DOI 10.1090/conm/183/02068
- Margit Rösler, Bessel-type signed hypergroups on $\textbf {R}$, Probability measures on groups and related structures, XI (Oberwolfach, 1994) World Sci. Publ., River Edge, NJ, 1995, pp. 292–304. MR 1414942
- Margit Rösler and Michael Voit, Partial characters and signed quotient hypergroups, Canad. J. Math. 51 (1999), no. 1, 96–116. MR 1692915, DOI 10.4153/CJM-1999-006-6
- Kenneth A. Ross, Signed hypergroups—a survey, Applications of hypergroups and related measure algebras (Seattle, WA, 1993) Contemp. Math., vol. 183, Amer. Math. Soc., Providence, RI, 1995, pp. 319–329. MR 1334786, DOI 10.1090/conm/183/02069
Additional Information
- Adam W. Parr
- Affiliation: Department of Mathematics, University of the Virgin Islands, St. Thomas, United States Virgin Islands
- Email: aparr@uvi.edu
- Received by editor(s): April 6, 2001
- Published electronically: March 13, 2002
- Communicated by: Andreas Seeger
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2661-2667
- MSC (2000): Primary 43A99
- DOI: https://doi.org/10.1090/S0002-9939-02-06513-9
- MathSciNet review: 1900874