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21.
22.
We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory. 相似文献
23.
Let Ω be a vector space over a finite field with q elements. Let G denote the general linear group of automorphisms of Ω and let us consider the left regular representation
associated with the natural action of G on the set X of linear subspaces of Ω. In this paper we study a natural basis B of the algebra EndG(L
2(X)) of intertwining maps on L
2(X). By using a Laplacian operator on Grassmann graphs, we identify the kernels in B as solutions of a basic hypergeometric difference equation. This provides two expressions for these kernels. One in terms
of the q-Hahn polynomials and the other by means of a Rodrigues type formula. Finally, we obtain a useful product formula for the
mappings in B. We give two different proofs. One uses the theory of classical hypergeometric polynomials and the other is supported by
a characterization of spherical functions in finite symmetric spaces. Both proofs require the use of certain associated Radon
transforms. 相似文献
24.
Pierre Jammes 《manuscripta mathematica》2007,123(1):15-23
Let M
n
be an n-dimensional compact manifold, with n ≥ 3. For any conformal class C of riemannian metrics on M, we set , where μ
p,k
(M,g) is the kth eigenvalue of the Hodge laplacian acting on coexact p-forms. We prove that . We also prove that if g is a smooth metric such that , and n = 0,2,3 mod 4, then there is a non-zero corresponding eigenform of degree with constant length. As a corollary, on a four-manifold with non vanishing Euler characteristic, there is no such smooth
extremal metric. 相似文献
25.
Jean Gillibert 《Mathematische Annalen》2007,338(2):475-495
The so-called class-invariant homomorphism ψ measures the Galois module structure of torsors—under a finite flat group scheme
G—which lie in the image of a coboundary map associated to an isogeny between (Néron models of) abelian varieties with kernel
G. When the varieties are elliptic curves with semi-stable reduction and the order of G is coprime to 6, it is known that the homomorphism ψ vanishes on torsion points. In this paper, using Weil restrictions of
elliptic curves, we give the construction, for any prime number p > 2, of an abelian variety A of dimension p endowed with an isogeny (with kernel μ
p
) whose coboundary map is surjective. In the case when A has rank zero and the p-part of the Picard group of the base is non-trivial, we obtain examples where ψ does not vanish on torsion points.
Résumé Le class-invariant homomorphism permet de mesurer la structure galoisienne des torseurs—sous un schéma en groupes fini et plat G—qui sont dans l’image du cobord associé à une isogénie, de noyau G, entre des (modèles de Néron de) variétés abéliennes. Quand les variétés sont des courbes elliptiques à réduction semi-stable et que l’ordre de G est premier à 6, on sait que cet homomorphisme s’annule sur les points de torsion. Dans cet article, en nous servant de restrictions de Weil de courbes elliptiques, nous construisons, pour tout nombre premier p > 2, une variété abélienne A de dimension p munie d’une isogénie (de noyau μ p ) dont le cobord est surjectif. Si A est de rang nul, et si la p-partie du groupe de Picard de la base est non triviale, nous obtenons ainsi un exemple où le class-invariant homomorphism ne s’annule pas sur les points de torsion.相似文献
26.
Marcinkiewicz Integrals with Non-Doubling Measures 总被引:2,自引:0,他引:2
Let μ be a positive Radon measure on
which may be non doubling. The only condition that μ must satisfy is μ(B(x, r)) ≤ Cr
n
for all
, r > 0 and some fixed constants C > 0 and n ∈ (0, d]. In this paper, we introduce the Marcinkiewicz integral related to a such measure with kernel satisfying some H?rmander-type
condition, and assume that it is bounded on L
2(μ). We then establish its boundedness, respectively, from the Lebesgue space L
1(μ) to the weak Lebesgue space L
1,∞(μ), from the Hardy space H
1(μ) to L
1(μ) and from the Lebesgue space L
∞(μ) to the space RBLO(μ). As a corollary, we obtain the boundedness of the Marcinkiewicz integral in the Lebesgue space L
p
(μ) with p ∈ (1,∞). Moreover, we establish the boundedness of the commutator generated by the RBMO(μ) function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger H?rmander-type condition, respectively,
from L
p
(μ) with p ∈ (1,∞) to itself, from the space L log L(μ) to L
1,∞(μ) and from H
1(μ) to L
1,∞(μ). Some of the results are also new even for the classical Marcinkiewicz integral.
The third (corresponding) author was supported by National Science Foundation for Distinguished Young Scholars (No. 10425106)
and NCET (No. 04-0142) of China. 相似文献
27.
Julianna S. Tymoczko 《Selecta Mathematica, New Series》2007,13(2):353-367
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology,
geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent
Hessenberg varieties for all classical types, generalizing results of De Concini–Lusztig–Procesi and Kostant. This paving
is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving
and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties
have no odd-dimensional homology.
相似文献
28.
Let
and
. We are interested in the lower bounds of the integral:
where h > 0 and
. Using the lower bounds for these integrals we obtain in particular for the so-called Fejér operator
of
the following asymptotic expression
which essentially improves the results concerning the approximation behavior of this operator.
Received: 10 January 2006 相似文献
29.
The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set
of a graph with maximal degree Δ is partitioned into sets V
i
of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each V
i
at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell,
on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of
ISR’s.
The research of the first author was supported by grant no 780/04 from the Israel Science Foundation, and grants from the
M. & M. L. Bank Mathematics Research Fund and the fund for the promotion of research at the Technion.
The research of the third author was supported by the Sacta-Rashi Foundation. 相似文献
30.
Alessandro Trombetta 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):65-78
In [11] Sion has investigated measures and integrals having values in uniform semigroups. In this paper a result which gives
sufficient conditions for the existence of a unique product of semigroup valued measures is established. Moreover a convergence
theorem for product integrals of semigroup valued functions is proved. 相似文献