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21.
22.
Nadya Gurevich 《Compositio Mathematica》2003,136(1):25-59
We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A
1×C
2 to generic representations of Spin7. Our construction uses the theta correspondence associated to the dual pair of the type (A
1×C
2
B
3) inside E
7. We also consider another theta correspondence associated to the dual pair of type (A
1×C
2
A
1×A
1) in D
6 and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold. 相似文献
23.
24.
The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a
univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially
in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the
joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends
and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms
that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726). 相似文献
25.
The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A
construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving
explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed
by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist
algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well
as complex reflection groups.
Received: July 25, 2001 相似文献
26.
Let Hn be an n-dimensional Haar subspace of
and let Hn−1 be a Haar subspace of Hn of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from Hn onto Hn−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1]. 相似文献
27.
Minoru Murata 《Journal of Functional Analysis》2007,245(1):177-212
We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M∂D×[0,T)), where M∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D). 相似文献
28.
Seppo Hassi Manfred Mö ller Henk de Snoo 《Proceedings of the American Mathematical Society》2006,134(10):2885-2893
The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.
29.
本文给出了分析多个相异性矩阵的三种方法.首先找到了一种图表示,使我们对所有相异性矩阵有一个总体的了解;其次定义了一个新的相异性矩阵,它可以看作是对所有原始相异性矩阵的一个折衷处理;最后提出了一种MIMU方法.在文中我们还对由上述方法得到的坐标图进行了比较. 相似文献
30.
We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT
c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y|
couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.). 相似文献