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Gabrielov's Rank Condition is Equivalent to an Inequality of Reduced Orders.

Shuzo Izumi — 1986

Mathematische Annalen

The Exterior Derivation and the Orders of Differential Forms on Contractible Algebras.

Shuzo Izumi — 1979

Mathematische Annalen

Note on convergence and orders of vanishing along curves.

Shuzo Izumi — 1990

Manuscripta mathematica

Linear Complementary Inequalities for Orders of Germs of Analytic Functions.

Shuzo Izumi

Inventiones mathematicae

Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals

Shuzo Izumi — 2015

Annales Polonici Mathematici

Let (U) denote the algebra of holomorphic functions on an open subset U ⊂ ℂⁿ and Z ⊂ (U) its finite-dimensional vector subspace. By the theory of least spaces of de Boor and Ron, there exists a projection $_{b}$ from the local ring $_{n, b}$ onto the space $Z_{b}$ of germs of elements of Z at b. At a general point b ∈ U its kernel is an ideal and $_{b}$ induces the structure of an Artinian algebra on $Z_{b}$ . In particular, this holds at points where the kth jets of elements of Z form a vector bundle for each k ∈ ℕ. For an embedded...

Restrictions of smooth functions to a closed subset

Shuzo Izumi — 2004

Annales de l’institut Fourier

We first provide an approach to the conjecture of Bierstone-Milman-Pawłucki on Whitney’s problem on $C^{d}$ extendability of functions. For example, the conjecture is affirmative for classical fractal sets. Next, we give a sharpened form of Spallek’s theorem on flatness.

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