Székelyhidi, László (2005) Discrete spectral synthesis Annales Mathematicae et Informaticae. 32. pp. 141-152. ISSN 1787-6117
pdf
AMI_32_from141to152.pdf Download (542kB) |
Absztrakt (kivonat)
Discrete spectral analysis and synthesis study the description of transla- tion invariant function spaces over discrete Abelian groups. The basic building bricks are the exponential monomials. A remarkable result of R. J. Elliot in 1965 claimed that spectral synthesis holds on any Abelian group, which means that the exponential monomials span a dense linear subspace in any pointwise-closed translation invariant linear space of complex valued functions over the group. Unfortunately, the proof of this theorem had several gaps. In this paper we give a short survey about the present status of discrete spectral analysis and synthesis, we show that Elliot’s theorem is false, we give a necessary condition for Abelian groups to have spectral synthesis and we formulate a conjecture about a possible characterization of Abelian groups having spectral synthesis. Key Words: spectral synthesis, torsion free rank, polynomial functions AMS Classification Number: 43A45, 39A70, 20K15
Mű típusa: | Folyóiratcikk | ||||||||
---|---|---|---|---|---|---|---|---|---|
Szerző: |
|
||||||||
Kapcsolódó URL-ek: | |||||||||
Nyelv: | angol | ||||||||
Kötetszám: | 32. | ||||||||
ISSN: | 1787-6117 | ||||||||
Felhasználó: | Tibor Gál | ||||||||
Dátum: | 10 Feb 2019 15:45 | ||||||||
Utolsó módosítás: | 10 Feb 2019 15:45 | ||||||||
URI: | http://publikacio.uni-eszterhazy.hu/id/eprint/2645 |
Tétel nézet |