共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we give the matrix characterizations from any normal vector-valued FK-space containing ø(X) into scalar-valued sequence space c(q) and by applying this result, we also obtain necessary and sufficient conditions for infinite matrices mapping the sequence spaces
, and Fr(X,p) into the space c(q), where p = (pk) and q = (qk) are bounded sequences of positive real numbers and r ≥ 0.AMS Subject Classification (2000): 46A45. 相似文献
2.
Jörg Eschmeier 《Archiv der Mathematik》2009,92(5):461-475
We use a variant of Grothendieck’s comparison theorem to show that, for a Fredholm tuple T ∈ L(X)n on a complex Banach space, there are isomorphisms . We conclude that a Fredholm tuple T ∈ L(X)n satisfies Bishop’s property (β) at z = 0 if and only if the vanishing conditions hold for . We apply these observations and results from commutative algebra to show that a graded tuple on a Hilbert space is Fredholm if and only if it satisfies Bishop’s property (β) at z = 0 and that, in this case, its cohomology groups can grow at most like kp.
Received: 14 January 2009 相似文献
3.
L. Olsen 《Monatshefte für Mathematik》2008,155(2):191-203
In this paper we consider the relationship between the topological dimension
and the lower and upper q-Rényi dimensions
and
of a Polish space X for q ∈ [1, ∞]. Let
and
denote the Hausdorff dimension and the packing dimension, respectively. We prove that
for all analytic metric spaces X (whose upper box dimension is finite) and all q ∈ (1, ∞); of course, trivially,
for all q ∈ [1, ∞]. As a corollary to this we obtain the following result relating the topological dimension and the lower and upper
q-Rényi dimensions:
for all Polish spaces X and all q ∈ [1, ∞]; in (1) and (2) we have used the following notation, namely, for two metric spaces X and Y, we write X ∼ Y if and only if X is homeomorphic to Y. Equality (1) has recently been proved for q = ∞ by Myjak et al.
Author’s address: Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland 相似文献
4.
Huan-song Zhou Hong-bo Zhu 《应用数学学报(英文版)》2007,23(4):685-696
In this paper,we consider the following ODE problem(P)where f ∈ C((0, ∞)×R,R),f(r,s)goes to p(r)and q(r)uniformly in r>0 as s→0 and s→ ∞,respectively,0≤p(r)≤q(r)∈ L~∞(0,∞).Moreover,for r>0,f(r,s)is nondecreasing in s≥0.Some existenceand non-existence of positive solutions to problem(P)are proved without assuming that p(r)≡0 and q(r)hasa limit at infinity.Based on these results,we get the existence of positive solutions for an elliptic problem. 相似文献
5.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
6.
In this paper, we consider the following singular nonlinear problem
where A is a positive continuous function on (0,1), q is a nonnegative measurable function on [0,1] and f is a nonnegative regular function on (0,1)×(0,).We suppose that
0
1
dt/A(t)< and 0<
0
1
A(t)q(t) dt<. Then we prove the existence and the uniqueness of a positive solution of this problem (P).Our approach is based on the use of the Green's function and the Schauder's fixed point theorem. 相似文献
7.
L. Olsen 《Monatshefte für Mathematik》2005,146(2):143-157
For a probability measure μ on a subset of
, the lower and upper Lq-dimensions of order
are defined by
We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions
and
. We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension
attains the smallest possible value and the upper Lq-dimension
attains the largest possible value. 相似文献
8.
A graph G with p vertices and q edges, vertex set V(G) and edge set E(G), is said to be super vertex-graceful (in short SVG), if there exists a function pair (f, f
+) where f is a bijection from V(G) onto P, f
+ is a bijection from E(G) onto Q, f
+((u, v)) = f(u) + f(v) for any (u, v) ∈ E(G),
and
We determine here families of unicyclic graphs that are super vertex-graceful.
相似文献
9.
Let f : X → Y be a morphism of pure-dimensional schemes of the same dimension, with X smooth. We prove that if is an arc on X having finite order e along the ramification subscheme R
f
of X, and if its image δ = f
∞(γ) on Y does not lie in J
∞(Y
sing), then the induced map T
γ
J
∞(X) → T
δ
J
∞(Y) is injective, with a cokernel of dimension e. In particular, if Y is smooth too, and if we denote by and the formal neighborhoods of and , then the induced morphism is a closed embedding of codimension e.
相似文献
10.
Giuseppe Maria Coclite Angelo Favini Gisèle Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Semigroup Forum》2008,77(1):101-108
The solution u of the well-posed problem
depends continuously on (a
ij
,β,γ,q).
Dedicated to Karl H. Hofmann on his 75th birthday. 相似文献
11.
J. Casado-Díaz T. Chacón Rebollo V. Girault M. Gómez Mármol F. Murat 《Numerische Mathematik》2007,105(3):337-374
In this paper we consider, in dimension d≥ 2, the standard finite elements approximation of the second order linear elliptic equation in divergence form with coefficients in L
∞(Ω) which generalizes Laplace’s equation. We assume that the family of triangulations is regular and that it satisfies an
hypothesis close to the classical hypothesis which implies the discrete maximum principle. When the right-hand side belongs
to L
1(Ω), we prove that the unique solution of the discrete problem converges in (for every q with ) to the unique renormalized solution of the problem. We obtain a weaker result when the right-hand side is a bounded Radon
measure. In the case where the dimension is d = 2 or d = 3 and where the coefficients are smooth, we give an error estimate in when the right-hand side belongs to L
r
(Ω) for some r > 1. 相似文献
12.
A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection , where every is a KTS(v) and all form a partition of all triples on X. In this article, we give a new construction for LKTS(6v + 3) via OLKTS(2v + 1) with a special property and obtain new results for LKTS, that is there exists an LKTS(3v) for , where p, q ≥ 0, r
i
, s
j
≥ 1, q
i
is a prime power and mod 12.
相似文献
13.
For κ ⩾ 0 and r0 > 0 let ℳ(n, κ, r0) be the set of all connected, compact n-dimensional Riemannian manifolds (Mn, g) with Ricci (M, g) ⩾ −(n−1) κ g and Inj (M) ⩾ r0. We study the relation between the kth eigenvalue λk(M) of the Laplacian associated to (Mn,g), Δ = −div(grad), and the kth eigenvalue λk(X) of a combinatorial Laplacian associated to a discretization X of M. We show that there exist constants c, C > 0 (depending only on n, κ and r0) such that for all M ∈ ℳ(n, κ, r0) and X a discretization of
for all k < |X|. Then, we obtain the same kind of result for two compact manifolds M and N ∈ ℳ(n, κ, r0) such that the Gromov–Hausdorff distance between M and N is smaller than some η > 0. We show that there exist constants c, C > 0 depending on η, n, κ and r0 such that
for all
.
Mathematics Subject Classification (2000): 58J50, 53C20
Supported by Swiss National Science Foundation, grant No. 20-101 469 相似文献
14.
V. F. Molchanov 《Acta Appl Math》2005,86(1-2):115-129
We define canonical representations for the hyperboloid of one sheet
and for the Lobachevsky space =G/K where G=SO0(1,n–1), H=SO0(1,n–2) and K=SO(n–1), as the restriction to G of representations associated with a cone of overgroups
and
for
and respectively. We determine explicitly the interaction of Lie operators of
with operators intertwining canonical representations and representations of G associated with a cone.Mathematics Subject Classifications (2000) 43A85, 22E46, 53D55.V. F. Molchanov: Supported by grants of the Netherlands Organization for Scientific Research (NWO): 047-008-009, the Russian Foundation for Basic Research (RFBR): 01-01-00100-a, the Minobr RF: E00-1.0-156, the NTP Univ. Rossii: ur04.01.037. 相似文献
15.
María J. Carro 《Mathematische Zeitschrift》2007,255(4):813-825
Given a sublinear operator T such that is bounded, it can be shown that is bounded, with constant C/(1−q), for every 0 < q < 1. In this paper, we study the converse result, not only for sequence spaces, but for general measure spaces proving that,
if T : L
q
(μ) → X is bounded, with constant C/(1−q), for every and X is Banach, then T : L log (1/L)(μ) → X is bounded. Moreover, this result is optimal. We also show that things are quite different if the Banach condition on X is dropped.
This work has been partially supported by MTM2004-02299 and by 2005SGR00556. 相似文献
16.
Andreas Greven 《Probability Theory and Related Fields》1990,85(3):307-364
Summary We study symmetric exclusion on a random set, where the underlying kernelp(x, y) is strictly positive. The random set is generated by Bernoulli experiments with success probabilityq.We prove that for certain values of the involved parameters the transport of particles through the system is drastically different from the classical situation on . In dimension one and
the transport of particles occurs on a nonclassical scale and is (on a macroscopic scale)not governed by the heat equation as in the case:r<|log(1-q)| on a random set, or in the classical situation on .The reason for this behaviour is, that a random walk with jump ratesp(x, y) restricted to the random set, converges to Brownian motion in the usual scaling ifr<|log(1-q)| but yields nontrivial limit behaviour only in the scalingxu
-1
x,tu
1+a
t(>) if + >r > |log(1-q)|. We calculate and study the limiting processes for the various scalings for fixed random sets. We shortly discuss the caser=+, here in general a great variety of scales yields nontrivial limits.Finally we discuss the case of a stationary random set. 相似文献
17.
Suthep Suantai 《Southeast Asian Bulletin of Mathematics》2000,24(2):297-303
In this paper, we give necessary and sufficient conditions for infinite matrices mapping from the Nakano vector-valued sequence space (X, p) into any BK-space, and by using this result, we obtain the matrix characterizations from (X, p) into the sequence spaces (Y), c0(Y, q), c(Y), s(Y), Er(Y), and Fr(Y), where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk 1 for all k N, r 0, and s 1.AMS Subject Classification (2000): 46A45 相似文献
18.
We obtain a new unimprovable Kolmogorov-type inequality for differentiable 2-periodic functions x with bounded variation of the derivative x, namely
where q (0, ), p [1, ], and = min{1/2, p/q(p + 1)}. 相似文献
19.
Let Λ be an algebraic set and let (n is even) be a polynomial mapping such that for each there is r(λ) > 0 such that the mapping g
λ = g(· , λ) restricted to the sphere S
n
(r) is an immersion for every 0 < r < r (λ), so that the intersection number I(g
λ|S
n
(r)) is defined. Then is an algebraically constructible function.
I. Karolkiewicz and A. Nowel supported by the grant BW/5100-5-0286-7. 相似文献
20.
Let V be a quadratic space with a form q over an arbitrary local field F of characteristic different from 2. Let with the form Q extending q with Q(e) = 1. Consider the standard embedding and the two-sided action of on . In this note we show that any -invariant distribution on is invariant with respect to transposition. This result was earlier proven in a bit different form in van Dijk (Math Z 193:581–593,
1986) for , in Aparicio and van Dijk (Complex generalized Gelfand pairs. Tambov University, 2006) for and in Bosman and van Dijk (Geometriae Dedicata 50:261–282, 1994) for p-adic fields. Here we give a different proof. Using results from Aizenbud et al. (arXiv:0709.1273 (math.RT), submitted), we
show that this result on invariant distributions implies that the pair (O(V), O(W)) is a Gelfand pair. In the archimedean setting this means that for any irreducible admissible smooth Fréchet representation
(π, E) of we have A stronger result for p-adic fields is obtained in Aizenbud et al. (arXiv:0709.4215 (math.RT), submitted). 相似文献