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61.
We compare and contrast various length vs Laplace spectra of compact flat Riemannian manifolds. As a major consequence we
produce the first examples of pairs of closed manifolds that are isospectral on p-forms for some p ≠ 0, but have different
weak length spectrum. For instance, we give a pair of 4-dimensional manifolds that are isospectral on p-forms for p = 1, 3and we exhibit a length of a closed geodesic that occurs in one manifold but cannot occur in the other. We also exhibit examples
of this kind having different injectivity radius and different first eigenvalue of the Laplace spectrum on functions. These
results follow from a method that uses integral roots of the Krawtchouk polynomials.
We prove a Poisson summation formula relating the p-eigenvalue spectrum with the lengths of closed geodesics. As a consequence
we show that the Laplace spectrum on functions determines the lengths of closed geodesics and, by an example, that it does
not determine the complex lengths. Furthermore we show that orientability is an audible property for closed flat manifolds.
We give a variety of examples, for instance, a pair of manifolds isospectral on functions (resp. Sunada isospectral) with
different multiplicities of length of closed geodesies and a pair with the same multiplicities of complex lengths of closed
geodesies and not isospectral on p-forms for any p, or else isospectral on p-forms for only one value of p ≠ 0. 相似文献
62.
Let {X, X
n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set
. Suppose lim
n→∞
and
, where d=2, if −1<b<0 and d>2(b+1), if b≥0. It is proved that, for any b>−1,
, where Γ(•) is a Gamma function.
Research supported by the National Natural Science Foundation of China (10071072). 相似文献
63.
Let R(t)=P(t)/Q(t) be a quotient of real polynomials. We show that ∫exp(iR(t)) dt/t has a uniform bound with a bound depending only on the degrees of P and Q and not on their coefficients. Also
LP estimates are obtained for certain associated singular integral operators. 相似文献
64.
In this paper a linearε-control problem for a general objective function is considered by functional analytic approach. Existence and uniqueness
of solutions are shown. The characterization of the solution is given in terms of a hyperplane. 相似文献
65.
Lina M. Mateus de Oliveira 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):224-240
IfA is a nest algebra andA
s=A ∩ A* , whereA* is the set of the adjoints of the operators lying inA, then the pair (A, A
s) forms a partial Jordan *-triple. Important tools when investigating the structure of a partial Jordan *-triple are its tripotents.
In particular, given an orthogonal family of tripotents of the partial Jordan *-triple (A, A
s), the nest algebraA splits into a direct sum of subspaces known as the Peirce decomposition relative to that family. In this paper, the Peirce
decomposition relative to an orthogonal family of minimal tripotents is used to investigate the structure of the inner ideals
of (A, A
s), whereA is a nest algebra associated with an atomic nest. A property enjoyed by inner ideals of the partial Jordan *-triple (A, A
s) is presented as the main theorem. This result is then applied in the final part of the paper to provide examples of inner
ideals. A characterization of the minimal tripotents as a certain class of rank one operators is also obtained as a means
to deduce the principal theorem. 相似文献
66.
John?J.?BenedettoEmail author Wojciech?Czaja Przemystaw?Gadziński Alexander?M.?Powell 《Journal of Geometric Analysis》2003,13(2):239-254
For any positive real numbers A, B, and d satisfying the conditions
, d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫ℝ|g(x)|2(1+|x|
A
)/log
d
(2+|x|)dx < ∞ and
. 相似文献
67.
A Littlewood-Paley type
inequality 总被引:2,自引:0,他引:2
In this note we prove the following theorem: Let u be a
harmonic function in the unit ball
and
. Then there is a
constant C =
C(p,
n) such that
. 相似文献
68.
We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved. 相似文献
69.
Richard Brown 《Geometriae Dedicata》2003,97(1):129-150
In this note, we show that given a closed, orientable genus-g surface S
g
, any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S
g
. To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism. 相似文献
70.