Displaying similar documents to “The product of n homogeneous forms”

Positively homogeneous functions and the Łojasiewicz gradient inequality

Alain Haraux (2005)

Annales Polonici Mathematici

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It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on ℝ N satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.

Besov spaces on spaces of homogeneous type and fractals

Dachun Yang (2003)

Studia Mathematica

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Let Γ be a compact d-set in ℝⁿ with 0 < d ≤ n, which includes various kinds of fractals. The author shows that the Besov spaces B p q s ( Γ ) defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p < ∞ and 1 ≤ q ≤ ∞.

Classifying homogeneous ultrametric spaces up to coarse equivalence

Taras Banakh, Dušan Repovš (2016)

Colloquium Mathematicae

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For every metric space X we introduce two cardinal characteristics c o v ♭ ( X ) and c o v ♯ ( X ) describing the capacity of balls in X. We prove that these cardinal characteristics are invariant under coarse equivalence, and that two ultrametric spaces X,Y are coarsely equivalent if c o v ♭ ( X ) = c o v ♯ ( X ) = c o v ♭ ( Y ) = c o v ♯ ( Y ) . This implies that an ultrametric space X is coarsely equivalent to an isometrically homogeneous ultrametric space if and only if c o v ♭ ( X ) = c o v ♯ ( X ) . Moreover, two isometrically homogeneous ultrametric spaces X,Y are coarsely equivalent if and...