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991.
We prove Knebusch’s Norm Principle for finite extensions of semi-local regular rings containing a field of characteristic 0. As an application we prove the Grothendieck-Serre conjecture on principal homogeneous spaces for the case of spinor groups of regular quadratic forms over a field of characteristic 0. 相似文献
992.
We study Riesz transforms associated with a sublaplacian H on a solvable Lie group G, where G has polynomial volume growth. It is known that the standard second order Riesz transforms corresponding to H are generally unbounded in Lp(G). In this paper, we establish boundedness in Lp for modified second order Riesz transforms, which are defined using derivatives on a nilpotent group GN associated with G. Our method utilizes a new algebraic approach which associates a distinguished choice of Cartan subalgebra with the sublaplacian
H. We also obtain estimates for higher derivatives of the heat kernel of H, and give a new proof (without the use of homogenization theory) of the boundedness of first order Riesz transforms. Our
results can be generalized to an arbitrary (possibly non-solvable) Lie group of polynomial growth. 相似文献
993.
In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided thatwhere Θ−1 is the inverse of the function Θ(t)=Φ(t)/t, and s is the “upper dimension” of the metric measure space. This condition is a generalization of a well known condition in Rn. For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided. 相似文献
994.
This paper concerns the problem of irreducible decompositions of unitary representations of topological groups G, including the group Diff0(M) of diffeomorphisms with compact support on smooth manifolds M. It is well known that the problem is affirmative, when G is a locally compact, separable group (cf. [3, 4]). We extend this result to infinite-dimensional groups with appropriate
quasi-invariant measures, and, in particular, we show that every continuous unitary representation of Diff0(M) has an irreducible decomposition under a fairly mild condition.
This research was partially supported by a Grant-in-Aid for Scientific Research (No.14540167), Japan Socieity of the Promotion
of Science. 相似文献
995.
996.
For any simply connected solvable Lie group Q of polynomial volume growth, we introduce the notion of nil-shadow of Q. We shall give an explicit formula for the distance to the origin of an element q ∈ Q in terms of its exponential coordinates of the second kind taken in an appropriate basis. This result extends a previous result for nilpotent Lie groups [6, Theorem DN] and [7, Theorem 1]. 相似文献
997.
We discuss the analysis of linear constant coefficient differential algebraic equations
on infinite dimensional Hilbert spaces. We give solution concepts and discuss solvability criteria which are mainly based
on Laplace transform. Furthermore, we investigate the decoupling of these systems motivated by the Kronecker normal form for
the finite dimensional case. Applications are given by the analysis of mixed systems of ordinary differential, partial differential
and differential algebraic equations. 相似文献
998.
The Fréchet distance between two multivariate normal distributions having means μX, μY and covariance matrices ΣX, ΣY is shown to be given by . The quantity d0 given by is a natural metric on the space of real covariance matrices of given order. 相似文献
999.
Peter Hall 《Journal of multivariate analysis》1982,12(3):432-449
We compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval—those based on Legendre polynomials, and on trigonometric functions. By examining the rates of convergence of their mean square errors we show that the Legendre polynomial estimators are superior in many respects. However, Legendre polynomial series can be more difficult to construct than trigonometric series, and to overcome this difficulty we show how to modify trigonometric series estimators to make them more competitive. 相似文献
1000.