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1.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
2.
We introduce o(p+1q+1)-invariant bilinear differential operators on the space of tensor densities on Rn generalizing the well-known bilinear sl2-invariant differential operators in the one-dimensional case, called Transvectants or Rankin–Cohen brackets. We also consider already known linear o(p+1q+1)-invariant differential operators given by powers of the Laplacian. 相似文献
3.
Let M be a smooth manifold,
the space of polynomial on fibers functions on T*M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M), of vector fields on M with coefficients in the space of linear differential operators on
. This cohomology space is closely related to the Vect(M)-modules,
(M), of linear differential operators on the space of tensor densities on M of degree . 相似文献
4.
I. Ovsienko T. Len L. Matzui Yu. Prylutskyy P. Eklund F. Normand U. Ritter P. Scharff 《Physica E: Low-dimensional Systems and Nanostructures》2007,37(1-2):78
The performed investigations permit to reveal the effect of giant magnetic resistance in the specimens of the compacted nanocarbon materials containing multi-walled carbon nanotubes modified with the transition metals (Fe and Co). 相似文献
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An increasing triangular mapping T on the n-dimensional cube Θ = [0, 1] n transforming a measure μ to a measure ν is considered, where μ and ν are absolutely continuous Borel probability measures having densities ρ μ and ρ ν . It is shown that if there exist positive constants ? and M such that ? < ρ ν < M, ? < ρ ν < M, there exist numbers α, β > 1 such that p = αβ(n ? 1)?1 (α + β)?1 > 1 and ρ μ ∈ W 1,α (Θ), ρ ν ∈ W 1,β ) (Θ), where W 1,q denotes a Sobolev class, then the mapping T belongs to the class W 1,p (Θ). 相似文献
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