2000
DOI: 10.1007/s002080050346
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The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets

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Cited by 9 publications
(10 citation statements)
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“…Here we generalize and strengthen the result in [1] by providing a proof which, among other things, also preserves definability.…”
Section: Introductionsupporting
confidence: 65%
See 1 more Smart Citation
“…Here we generalize and strengthen the result in [1] by providing a proof which, among other things, also preserves definability.…”
Section: Introductionsupporting
confidence: 65%
“…In [1], Acquistapace, Andradas and Broglia proved the strict Positivstellensatz for (global) analytic functions on Euclidean spaces.…”
Section: Introductionmentioning
confidence: 99%
“…By Whitney's approximation theorem ([13, Section 1.6]), there exists an analytic function η : R n !R such that |σ 2 ϕ+1−η|< 1 2 on R n . Let us see that…”
Section: Preliminary Resultsmentioning
confidence: 99%
“…Others have made improvements of the above theorem. Acquistapace et al [1] found a strict analytical positivstellensatz where K needs not be compact, but f remains strictly positive on K. We cannot obtain Schmüdgen-type results without strict positivity unless we add additional hypotheses. This paper gives an instance of additional hypotheses which leads to results of Schmüdgen type without strict positivity.…”
Section: Introductionmentioning
confidence: 88%
“…Then for each factor of even degree, its degree will be the degree of its representation. And, for each factor of odd degree, we showed in the first part of Theorem 2 that the degree of the representation will be twice the degree of the factor (see (1) and (2) i=1 to a 1 . Our first step will be to represent this in S{1 − x 2 }.…”
Section: Elizabeth Mauch This Will Give Us a Valid Representation Ofmentioning
confidence: 97%