共查询到20条相似文献,搜索用时 15 毫秒
1.
Daniel W. Cunningham 《Archive for Mathematical Logic》2007,46(3-4):197-221
The Dodd–Jensen Covering Lemma states that “if there is no inner model with a measurable cardinal, then for any uncountable set of ordinals X, there is a ${Y\in K}$ such that ${X\subseteq Y}$ and |X| = |Y|”. Assuming ZF+AD alone, we establish the following analog: If there is no inner model with an ${\mathbb {R}}$ –complete measurable cardinal, then the real core model ${K(\mathbb {R})}$ is a “very good approximation” to the universe of sets V; that is, ${K(\mathbb {R})}$ and V have exactly the same sets of reals and for any set of ordinals X with ${|{X}|\ge\Theta}$ , there is a ${Y\in K(\mathbb {R})}$ such that ${X\subseteq Y}$ and |X| = |Y|. Here ${\mathbb {R}}$ is the set of reals and ${\Theta}$ is the supremum of the ordinals which are the surjective image of ${\mathbb {R}}$ . 相似文献
2.
Daniel W. Cunningham 《Archive for Mathematical Logic》2012,51(3-4):319-351
Using a Levy hierarchy and a fine structure theory for ${K(\mathbb{R})}$ , we obtain scales of minimal complexity in this inner model. Each such scale is obtained assuming the determinacy of only those sets of reals whose complexity is strictly below that of the scale constructed. 相似文献
3.
Francisco Martin Masaaki Umehara Kotaro Yamada 《Calculus of Variations and Partial Differential Equations》2009,36(1):119-139
We construct a simply connected complete bounded mean curvature one surface in the hyperbolic 3-space ${\mathcal {H}^3}$ . Such a surface in ${\mathcal {H}^3}$ can be lifted as a complete bounded null curve in ${\rm {SL}(2,\mathbb {C})}$ . Using a transformation between null curves in ${\mathbb {C}^3}$ and null curves in ${\rm {SL}(2,\mathbb {C})}$ , we are able to produce the first examples of complete bounded null curves in ${\mathbb {C}^3}$ . As an application, we can show the existence of a complete bounded minimal surface in ${\mathbb {R}^3}$ whose conjugate minimal surface is also bounded. Moreover, we can show the existence of a complete bounded immersed complex submanifold in ${\mathbb {C}^2}$ . 相似文献
4.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces
Lw2(\mathbbR){L_{\omega}^{2}(\mathbb{R})} For operators M in the algebra generated by the convolutions with
f ? Cc(\mathbb R){\phi \in {C_c(\mathbb {R})}} we show that [`(m(W))] = s(M){\overline{\mu(\Omega)} = \sigma(M)}, where the set Ω is determined by the spectrum of the shift S and μ is the symbol of M. For the general multipliers M we establish that [`(m(W))]{\overline{\mu(\Omega)}} is included in σ(M). A generalization of these results is given for the weighted spaces
L2w(\mathbb Rk){L^2_{\omega}(\mathbb {R}^{k})} where the weight ω has a special form. 相似文献
5.
A submeasure μ defined on the subsets of is nonatomic if for every ℓ ≥ 1 there exists a partition of into a finite number of parts on which μ is bounded from above by 1/ℓ. In this paper we answer several natural questions concerning nonatomic submeasures d
F
that are determined (like the standard density) by a family F of finite subsets of . We first show that if the number of n-element sets in F grows at most exponentially with n, then d
F
is nonatomic; but if this growth condition fails, then d
F
need not be nonatomic in general. We next prove that, for a nonatomic submeasure d
F
, the minimal number of sets in a 1/ℓ-small partition of can grow arbitrarily fast with ℓ. We also give a simple example of a nonatomic submeasure that is not equivalent to a submeasure of type d
F
.
The second author acknowledges a generous support of the Foundation for Polish Science. 相似文献
6.
7.
We show that a cuspidal normalized Hecke eigenform g of level one and even weight is uniquely determined by the central values of the family of Rankin– Selberg L-functions \({L(s, f\otimes g)}\) , where f runs over the Hecke basis of the space of cusp forms of level one and weight k with k varying over an infinite set of even integers. 相似文献
8.
In our earlier paper (Arch. Math. 91 (2008), 76–85), we proved that if F is a sequence of finite nonempty subsets of such that a certain quantity t(F) is finite, then the associated submeasure dF on is nonatomic. In the present note, we give two curious characterizations of the set of such sequences F.
The second author is partially supported by the Foundation for Polish Science. 相似文献
9.
Yixin Yang 《Integral Equations and Operator Theory》2013,77(2):279-290
Let M be a shift invariant subspace in the vector-valued Hardy space ${H_{E}^{2}(\mathbb{D})}$ H E 2 ( D ) . The Beurling–Lax–Halmos theorem says that M can be completely characterized by ${\mathcal{B}(E)}$ B ( E ) -valued inner function ${\Theta}$ Θ . When ${E = H^{2}(\mathbb{D}),\,H_{E}^{2}(\mathbb{D})}$ E = H 2 ( D ) , H E 2 ( D ) is the Hardy space on the bidisk ${H^{2}(\mathbb{D}^2)}$ H 2 ( D 2 ) . Recently, Qin and Yang (Proc Am Math Soc, 2013) determines the operator valued inner function ${\Theta(z)}$ Θ ( z ) for two well-known invariant subspaces in ${H^{2}(\mathbb{D}^{2})}$ H 2 ( D 2 ) . This paper generalizes the ${\Theta(z)}$ Θ ( z ) by Qin and Yang (Proc Am Math Soc, 2013) and deal with the structure of ${M = {\Theta}(z)H^{2}(\mathbb{D}^{2})}$ M = Θ ( z ) H 2 ( D 2 ) when M is an invariant subspace in ${H^{2}(\mathbb{D}^{2})}$ H 2 ( D 2 ) . Unitary equivalence, spectrum of the compression operator and core operator are studied in this paper. 相似文献
10.
P. W. Ng 《Integral Equations and Operator Theory》2016,86(1):13-40
Let \({C^*_r(\mathbb{F}_{\infty})}\) be the reduced C*-algebra of the free group on infinitely many generators. Say that \({a, b \in C^*_r(\mathbb{F}_{\infty})_{SA}}\). Then \({a}\) is majorized by \({b}\) if and only if \({a \in \overline{Conv(U(b))}.}\) In particular, \({\tau(b)1 \in \overline{Conv(U(b))}.}\) Moreover, in the above results, we provide uniform bounds for the number of unitary conjugates needed for a given approximation. In the above, \({Conv(U(b))}\) is the convex hull of the unitary orbit of \({b}\) in \({C^*_r(\mathbb{F}_{\infty})}\). 相似文献
11.
We show that positive isometric averaging operators on the sequence space \({\ell^2(\mathbb{Z}, \mu)}\) are determined by very subtle arithmetic conditions on \({\mu}\) (even for very simple examples), contrary to what happens in the continuous case \({L^2({\mathbb{R}}^+)}\), where any possible average value is realized by a suitable positive isometry. 相似文献
12.
T. R. Riley 《Geometriae Dedicata》2005,113(1):215-229
We give a nondeterministic algorithm that expresses elements of
, for N ≥ 3, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We show that the nondeterministic time-complexity of the subtractive version of Euclid’s algorithm for finding the greatest common divisor of N ≥ 3 integers a1, ..., aN is at most a constant times
. This leads to an elementary proof that for N ≥ 3 the word metric in
is biLipschitz equivalent to the logarithm of the matrix norm – an instance of a theorem of Mozes, Lubotzky and Raghunathan. And we show constructively that there exists K>0 such that for all N ≥ 3 and primes p, the diameter of the Cayley graph of
with respect to the generating set
is at most
.Mathematics Subject Classification: 20F05 相似文献
13.
14.
Daniel Arnaudon N. Crampé Anastasia Doikou Luc Frappat Eric Ragoucy 《Annales Henri Poincare》2006,7(7-8):1217-1268
We consider the N-site
integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe
ansatz techniques we are able to determine the spectrum and the corresponding Bethe ansatz equations for the general case,
where each site of the spin chain is associated to any representation of
In the case of open spin chain, we study finite dimensional representations of the quantum reflection algebra, and prove in
full generality that the pseudo-vacuum is a highest weight of the monodromy matrix.
For these two types of spin chain, we study the (generalized) “algebraic” fusion procedures, which amount to construct the
quantum contraction and the Sklyanin determinant for the
and quantum reflection algebras. We also determine the symmetry algebra of these two types of spin chains, including general
K and K+ diagonal matrices for the open case.
The case of open spin chains with soliton non-preserving boundary conditions is also presented in the framework of quantum
twisted Yangians. The symmetry algebra of this spin chains is studied. We also give an exhaustive classification of the invertible
matricial solutions to the corresponding reflection equation.
Communicated by Petr Kulish
Dedicated to our friend Daniel Arnaudon
Submitted: December 12, 2005; Accepted: January 23, 2006 相似文献
15.
B. Bouchard 《Journal of Theoretical Probability》2005,18(2):439-467
Motivated by applications in financial mathematics, Ref. 3 showed that, although
fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of
: if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extended by Ref. 1 in the multidimensional case, replacing
by a closed convex cone K of [0, )d, and by Ref. 12 who provided a conditional version in the unidimensional case. In this paper, we show that the conditional bipolar theorem of Ref. 12 can be extended to the multidimensional case. Using a decomposition result obtained in Ref. 3 and Ref. 1, we also remove the boundedness assumption of Ref. 12 in the one dimensional case and provide less restrictive assumptions in the multidimensional case. These assumptions are completely removed in the case of polyhedral cones K. 相似文献
16.
17.
Apoloniusz Tyszka 《Journal of Geometry》2006,85(1-2):188-199
18.
We prove real Paley-Wiener type theorems for the Dunkl transform ℱ
D
on the space
of tempered distributions. Let T∈S′(ℝ
d
) and Δ
κ
the Dunkl Laplacian operator. First, we establish that the support of ℱ
D
(T) is included in the Euclidean ball
, M>0, if and only if for all R>M we have lim
n→+∞
R
−2n
Δ
κ
n
T=0 in S′(ℝ
d
). Second, we prove that the support of ℱ
D
(T) is included in ℝ
d
∖B(0,M), M>0, if and only if for all R<M, we have lim
n→+∞
R
2n
ℱ
D
−1(‖y‖−2n
ℱ
D
(T))=0 in S′(ℝ
d
). Finally, we study real Paley-Wiener theorems associated with
-slowly increasing function.
相似文献
19.
In this paper, we obtain sufficient and necessary conditions for a simply connected Riemannian manifold (M n , g) to be isometrically immersed into ${\mathbb{S}^m \times \mathbb{R}}$ and ${\mathbb{H}^m \times \mathbb{R}}$ . 相似文献
20.
Todd Kemp 《Journal of Theoretical Probability》2017,30(2):397-451
This paper studies the empirical laws of eigenvalues and singular values for random matrices drawn from the heat kernel measures on the unitary groups \({\mathbb {U}}_N\) and the general linear groups \({\mathbb {GL}}_N\), for \(N\in {\mathbb {N}}\). It establishes the strongest known convergence results for the empirical eigenvalues in the \({\mathbb {U}}_N\) case, and the first known almost sure convergence results for the eigenvalues and singular values in the \({\mathbb {GL}}_N\) case. The limit noncommutative distribution associated with the heat kernel measure on \({\mathbb {GL}}_N\) is identified as the projection of a flow on an infinite-dimensional polynomial space. These results are then strengthened from variance estimates to \(L^p\) estimates for even integers p. 相似文献