• Corpus ID: 119312292

Peetre-Slovak's theorem revisited

@inproceedings{Navarro2014PeetreSlovaksTR,
  title={Peetre-Slovak's theorem revisited},
  author={Jos'e Navarro and Juan Blanco Sancho},
  year={2014}
}
AbstractIn 1960, J. Peetre proved the finiteness of the order of linear local operators. Lateron, J. Slov´ak vastly generalized this theorem, proving the finiteness of the order of abroad class of (non-linear) local operators.In this paper, we use the language of sheaves and ringed spaces to prove a simplerversion of Slov´ak’s result. The statement we prove deals with local operators definedbetween the sheaves of smooth sections of fibre bundles, and thus covers many of theapplications of Slov´ak’s… 
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References

SHOWING 1-10 OF 21 REFERENCES
Peetre Theorem for Nonlinear Operators
Some generalizations of the well-known Peetre theorem on the locally finite order of support non-increasing R-linear operators, [9, 11], has become a useful tool for various geometrical
ON INVARIANT OPERATIONS ON A MANIFOLD WITH CONNECTION OR METRIC
The study of the invariant local operations on exterior forms is a classical and well understood subject. However, we reconsider the problem assuming only the locality of the operations and we still
On the Theorem of Ошкин
In this paper the normality of a family of holomorphic functions is studied and the following result is obtained:Theorem 1 Suppose is a family of holomorphic function in a domain D.n,k(≥2) are
Natural operations in differential geometry
I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.
Local cohomology of the algebra of C∞ functions on a connected manifold
A multilinear version of Peetre's theorem on local operators is the key to prove the equality between the local and differentiable Hochschild cohomology on the one hand, and on the other hand the
Energy and electromagnetism of a differential form
Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as
On the naturalness of Einstein’s equation
We compute all 2-covariant tensors naturally constructed from a semiriemannian metric g which are divergence-free and have weight greater than 2. As a consequence, it follows a characterization of
Natural operators related with the variational calculus
The Euler and Poincare-Cartan morphisms of the variational calculus in fibered manifolds are characterized from the naturality point of view.
Natural operations on differential forms, Diff
  • Geom. Appl. 38,
  • 2015
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