Gabrielov's Rank Condition is Equivalent to an Inequality of Reduced Orders.
The Exterior Derivation and the Orders of Differential Forms on Contractible Algebras.
Note on convergence and orders of vanishing along curves.
Linear Complementary Inequalities for Orders of Germs of Analytic Functions.
Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals
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 from the local ring onto the space of germs of elements of Z at b. At a general point b ∈ U its kernel is an ideal and induces the structure of an Artinian algebra on . 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
We first provide an approach to the conjecture of Bierstone-Milman-Pawłucki on Whitney’s problem on 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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