Abstract
Abstract We introduce a concept of hereditary set of multi-indices, and consider vector spaces of functions generated by families associated to such sets of multi-indices, called hereditary function spaces. Existence and uniquenes of representing measures for some abstract truncated moment problems are investigated in this framework, by adapting the concept of idempotent and that of dimensional stability, and using some techniques involving C*-algebras and commuting self-adjoint multiplication operators.
Highlights
We introduce a concept of hereditary set of multi-indices, and consider vector spaces of functions generated by families associated to such sets of multi-indices, called hereditary function spaces
Existence and uniquenes of representing measures for some abstract truncated moment problems are investigated in this framework, by adapting the concept of idempotent and that of dimensional stability, and using some techniques involving C*-algebras and commuting self-adjoint multiplication operators
The use of nite families of multi-indices with appropriate properties to investigate the associated truncated moment problems appears in several works, as for instance in [8, 9], and more recently in [17, 18]
Summary
The use of nite families of multi-indices with appropriate properties to investigate the associated truncated moment problems appears in several works, as for instance in [8, 9], and more recently in [17, 18]. For the assignment tk → γk, which induces a linear functional on PKn , say ΛK, one looks for a non-negative measure μ on B(Rn) such that ΛK(p) = p(t)dμ(t) for all p ∈ PKn. The moment problems with respect to a given set of multi-indices K can be stated in a more abstract context, for functions more general that polynomials. The moment problems with respect to a given set of multi-indices K can be stated in a more abstract context, for functions more general that polynomials Let us introduce such a convenient framework. Rstly stated for polynomial moment problem (see [5]) is still very useful in our more general framework Speci cally, it insures the uniqueness of the representing measure when such a measure exists (see Proposition 1).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
