منابع مشابه
Blow-analytic Equivalence of Two Variable Real Analytic Function Germs
Blow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop the real analytic equisingularity theory. In this paper we give several complete characterisations of blow-analytic equivalence in the two dimensional case in terms of the minimal resolutions, the real tree model for the arrangement of Newton-Puiseux roots, and the cascade blo...
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We determine all complete intersection surface germs whose Pythagoras number is 2, and find they are all embedded in R and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these properties for mixed surface germs in R. Finally, we find in higher embedding dimension three different familie...
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Two subanalytic subsets of Rn are s-equivalent at a common point, say O, if the Hausdorff distance between their intersections with the sphere centered at O of radius r goes to zero faster than rs. In the present paper we investigate the existence of an algebraic representative in every sequivalence class of subanalytic sets. First we prove that such a result holds for the zero-set V (f) of an ...
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We show that: (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1972-0313545-7