New topological C-algebras with applications in linear systems theory

Daniel Alpay, Guy Salomon

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Motivated by the Schwartz space of tempered distributions ℓ′ and the Kondratiev space of stochastic distributions S -1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′ p ∈ N, with decreasing norms ||·|| p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form ||f * g|| p ≤ A(p-q)||f|| q||g|| p for all p < q + d, where * denotes the convolution in the monoid, A(p-q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an inequality holds in S -1, but not in ℓ′. We give an example of such a ring which contains ℓ′. We characterize invertible elements in these rings and present applications to linear system theory.

Original languageEnglish
Article number1250011
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume15
Issue number2
DOIs
StatePublished - 1 Jun 2012

Keywords

  • Kondratiev spaces
  • Nuclear spaces
  • Schwartz space of tempered distributions
  • Våge inequality
  • Wick product
  • convolution
  • linear systems on commutative rings
  • topological rings
  • white noise space

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'New topological C-algebras with applications in linear systems theory'. Together they form a unique fingerprint.

Cite this