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911.
We present two approaches to the spectral studies for infinite Jacobi matrices with monotonic or near-to-monotonic weights. The first one is based on the subordination theory due to Khan and Pearson [17] combined with the detailed analysis of the transfer matrices for the solutions of the formal eigenequation. The second one uses an extension of the commutator approach developed by Putnam in [19]. Applying these methods we prove the absolute continuity for several classes of weights and diagonals. For some other cases we prove the emptiness of the point spectrum. The results are illustrated with examples and compared with the results of Dombrowski [7]-[13], Clark [2] and of Máté and Nevai [18]. We show that some of our results are stronger.The research of the first author has been supported by the KBN grant PB 2 P03A 002 13. 相似文献
912.
Marcinkiewicz integral on hardy spaces 总被引:14,自引:0,他引:14
In this paper we prove that the Marcinkiewicz integral is an operator of type (H
1,L
1) and of type (H
1,,L
1,). As a corollary of the results above, we obtain again the the weak type (1,1) boundedness of , but the smoothness condition assumed on is weaker than Stein's condition.The research was supported partly by Doctoral Programme Foundation of Institution of Higher Education (Grant No. 98002703) of China.The author was supported partly by NSF of China (Grant No. 19971010).The author was supported partly by NSF of China (Grant No. 19131080). 相似文献
913.
Let ƒ and g be real-analytic functions near the origin in ℝ2. Given 1 < p < ∞, we obtain a characterization of the set of positive numbers ∈ and δ that ensures
for some small neighborhood K of the origin. A notion of stability is introduced in relation to Ap weights and a counterexample is presented to show that the two-dimensional weighted problem, unlike its analog in dimension
one, is not stable. 相似文献
914.
We define the Hopf algebra structure on the Grothendieck group of finite-dimensional polynomial representations of
in the limitN→∞. The resulting Hopf algebra Rep
is a tensor product of its Hopf subalgebras Repa
,a ∈ ℂ×/q2ℤ. Whenq is generic (resp.,q
2 is a primitive root of unity of orderl), we construct an isomorphism between the Hopf algebra Rep
a
and the algebra of regular functions on the prounipotent proalgebraic group
(resp.,
). Whenq is a root of unity, this isomorphism identifies the Hopf subalgebra of Rep
a
spanned by the modules obtained by pullback with respect to the Frobenius homomorphism with the algebra generated by the
coefficients of the determinant of an element of
considered as anl×l matrix over the Taylor series. This gives us an explicit formula for the Frobenius pullbacks of the fundamental representations.
In addition, we construct a natural action of the Hall algebra associated to the infinite linear quiver (resp., the cyclic
quiver withl vertices) on Rep
a
and describe the span of tensor products of evaluation representations taken at fixed points as a module over this Hall algebra. 相似文献
915.
916.
917.
HuangWenhua ShenZuhe 《高校应用数学学报(英文版)》1999,14(2):131-136
An existence and uniqueness result concerned with the Diriehlet boundary value prob-lem u“ cu‘ g(t,u)=e(t),u(0)=u(π)=0 is offered. 相似文献
918.
R. S. Garibaldi 《manuscripta mathematica》1999,98(1):97-113
Let F be a field of characteristic ≠ 2 such that is of cohomological 2- and 3-dimension ≤ 2. For G a simply connected group of type 3
D
4 or 6
D
4 over F, we show that the natural map
where Ω
F
is the set of orderings of F and F
v
denotes the completion of F at v, restricts to be injective on the image of H
1(F, Z(G)) in H
1(F, G).
For F not formally real, this implies that Serre's “Conjecture II” [Ser.94,III.3.1] holds for such groups if and only if trialitarian
groups are classified by their Tits algebras over F.
Received: 17 September 1998 相似文献
919.
A subset S of a d-dimensional convex body K is extensive if S
∂K and for any p, q ∈ S the distance between p and q is at least one-half of the maximum length of chords of K parallel to the segment pq. In this paper we establish the general upper bound |S| ≤ 3
d
— 1. We also find an upper bound for a certain class of 3-polytopes, which leads to the determination of the maximum cardinalities
of extensive subsets and their extremal configurations for tetrahedra, octahedra and some other 3-polytopes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
920.
Daoxing Xia 《Integral Equations and Operator Theory》1999,33(4):489-506
This paper studies the class of pure operatorsA on a Hilbert space
satisfying dimK
A
<, where
. The main tool is a pair of matrices
and
. A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class. 相似文献