Displaying similar documents to “Multivariate moment problems : geometry and indeterminateness”

Geometry of Puiseux expansions

Maciej Borodzik, Henryk Żołądek (2008)

Annales Polonici Mathematici

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We consider the space Curv of complex affine lines t ↦ (x,y) = (ϕ(t),ψ(t)) with monic polynomials ϕ, ψ of fixed degrees and a map Expan from Curv to a complex affine space Puis with dim Curv = dim Puis, which is defined by initial Puiseux coefficients of the Puiseux expansion of the curve at infinity. We present some unexpected relations between geometrical properties of the curves (ϕ,ψ) and singularities of the map Expan. For example, the curve (ϕ,ψ) has a cuspidal singularity iff it...

On fractals which are not so terrible

António M. Caetano (2002)

Fundamenta Mathematicae

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The notion of NST domain and the closely related notion of ball condition, both topological in nature and quite useful within the theory of function spaces, are compared with each other (and with the older concept of porosity) and also with other notions of interest, like those of d-set and of interior regular domain, which have a measure-theoretical nature. Also, after extending the idea of NST (not so terrible) to a larger class of sets, the property is studied in the context of anisotropic...

Continuous dependence on parameters of certain self-affine measures, and their singularity

Daoxin Ding (2011)

Czechoslovak Mathematical Journal

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In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.