Redaktion: K. Sigmund, G. Greschonig (Univ. Wien, Strudlhofgasse ...

Funktionalanalysis, Harmonische Analysis 123
[1] C.Lizama : On the convergence and Approxiamtion of Integrated Semigroups.
J.Math.Anal.Appl.181, No1, 89-103 (1994)
[2] S.Nicaise : The Hille-Yosida and Trotter-Kato Theorems for Integrated Semigroups.
J.Math.Anal.Appl.180, No2, 303-316 (1993)
Sequence spaces with exponent weights, Realisations of
Colombeau type algebras
STEVAN PILIPOVIĆ
(gemeinsam mit A. Delcroix, M. Hasler, V. Valmorin)
Institute of Mathematics, Faculty of Sciences, University of Novi Sad
Trg D. Obradovica 4, 21 000 Novi Sad, Yu
pilipovic@unsim.ns.ac.yu
http://www.im.ns.ac.yu
Colombeau had constructed his well-known algebras by algebraic methods. No
topology had appeared in his construction. Our aim is to give a purely topological
description of Colombeau type algebras. We show that such algebras fit very
well in the general theory of the well known sequence spaces forming appropriate
algebras. All these classes of algebras are simply determined by the (locally convex)
space E and a sequence of weights r : N � R� which serves to construct an
ultrametric on the sequence space E N . The sequence r � � rn� n is assumed to be
decreasing to zero. This implies that sequence spaces under consideration (� E N )
contain as a subspace E � diagE N and that they induce the discrete topology on
E. Our analysis implies that if one has a Colombeau type algebra containing the
Dirac delta distribution as an embedded Colombeau generalized function, then
the topology induced on the basic space must be discrete. This is an analogous
result to the Schwartz’s “imposibility result” concerning the product of distributions.
A major part of the talk is devoted to embeddings of ultradistribution and
hyperfunction spaces into corresponding classes of sequence spaces.
[1] Colombeau, J. F.: Multiplication of Distributions Lect. Not. Math. 1532,
Springer, Berlin, 1992.
[2] Oberguggenberger, M.: Multiplication of Distributions and Applications to
Partial Differential Equations, Pitman Res. Not. Math. 259, Longman Sci.
Techn., Essex, 1992.
[3] Pilipović, S.: Colombeau’s generalized functions and pseudodifferential operators,
University of Tokio, Lecture Notes Series, 1994.
[4] Pilipović. S., Scarpalezos, D.: Colombeau generalized Ultradistributions,
Math. Proc. Camb. Phil Soc., 130(2001), 541-553.