Bulletin of the Belgian Mathematical Society - Simon Stevin

Substructures in algebras of associated homogeneous distributions on $R$

Ghislain R. Franssens

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Abstract

In previous work the author constructed a convolution algebra and an isomorphic multiplication algebra of one-dimensional associated homogeneous distributions with support in $R$. In this paper we investigate the various algebraic substructures that can be identified in these algebras. Besides identifying ideals and giving polynomial representations for six subalgebras, it is also shown that both algebras contain an interesting Abelian subgroup, which can be used to construct generalized integration/derivation operators of complex degree on the whole line $R$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 1 (2012), 137-153.

Dates
First available in Project Euclid: 7 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1331153414

Digital Object Identifier
doi:10.36045/bbms/1331153414

Mathematical Reviews number (MathSciNet)
MR2952801

Zentralblatt MATH identifier
1248.46031

Subjects
Primary: 46F10: Operations with distributions 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}

Keywords
Associated Homogeneous Distribution Convolution Algebra Multiplication Algebra

Citation

Franssens, Ghislain R. Substructures in algebras of associated homogeneous distributions on $R$. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 1, 137--153. doi:10.36045/bbms/1331153414. https://projecteuclid.org/euclid.bbms/1331153414


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