共查询到20条相似文献,搜索用时 27 毫秒
1.
Nikolaos D. Atreas 《Advances in Computational Mathematics》2012,36(1):21-38
Let ϕ be a function in the Wiener amalgam space W¥(L1)\emph{W}_{\infty}(L_1) with a non-vanishing property in a neighborhood of the origin for its Fourier transform [^(f)]\widehat{\phi},
t={tn}n ? \mathbb Z{\bf \tau}=\{\tau_n\}_{n\in {{\mathbb Z}}} be a sampling set on ℝ and VftV_\phi^{\bf \tau} be a closed subspace of
L2(\mathbbR)L_2(\hbox{\ensuremath{\mathbb{R}}}) containing all linear combinations of τ-translates of ϕ. In this paper we prove that every function f ? Vftf\in V_\phi^{\bf \tau} is uniquely determined by and stably reconstructed from the sample set
Lft(f)={ò\mathbbR f(t)[`(f(t-tn))] dt}n ? \mathbb ZL_\phi^{\bf \tau}(f)=\Big\{\int_{\hbox{\ensuremath{\mathbb{R}}}} f(t) \overline{\phi(t-\tau_n)} dt\Big\}_{n\in {{\mathbb Z}}}. As our reconstruction formula involves evaluating the inverse of an infinite matrix we consider a partial reconstruction
formula suitable for numerical implementation. Under an additional assumption on the decay rate of ϕ we provide an estimate to the corresponding error. 相似文献
2.
Fred B. Weissler 《Israel Journal of Mathematics》1978,29(2-3):265-275
Under certain circumstances, the Trotter-Lie formulaW
t=lim(U
t/nVt/n)
n
is used to construct a non-linear semi-groupW
t on closed subsets ofL
P, 1≦p<∞. In particular we consider the situation whereU
t=e
tA is a positivity preservingC
0 (linear) semi-group andV
t is generated by a (non-linear) functionF with certain monotonicity properties. In general,A andF are “singular” onL
p and no requirement is made that one of them be “relatively bounded” with respect to the other. The generator of the resulting
semi-groupW
t turns out to be an extension ofA +F restricted to a suitable domain.
Research supported by a Danforth Graduate Fellowship and a Weizmann Postdoctoral Fellowship. 相似文献
3.
Optimal constant weight covering codes and nonuniform group divisible 3-designs with block size four
Let K
q
(n, w, t, d) be the minimum size of a code over Z
q
of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this article, we determine K
q
(n, 4, 3, 1) for all n ≥ 4, q = 3, 4 or q = 2
m
+ 1 with m ≥ 2, leaving the only case (q, n) = (3, 5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames, which play a crucial role
in the recursive constructions of group divisible 3-designs similar to that of candelabra systems in the constructions of
3-wise balanced designs. As an application of this approach, several new infinite classes of nonuniform group divisible 3-designs
with block size four are also constructed. 相似文献
4.
Suppose W is a Weyl group with Φ = Φ(W) a root system of W. The set D of root differences is given by D = {α − β : α, β, ∈ Φ}. We define t(Φ) to be the maximum exponent of the torsion subgroup of
for any
In this article we show that if W is of type An, then t(Φ) = 2n.
Received: 25 November 2004 相似文献
5.
Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S
4 denote the symmetric group on 4 letters. We determine the universal deformation ring R(S
4,V) for every kS
4-module V which has stable endomorphism ring k and show that R(S
4,V) is isomorphic to either k, or W[t]/(t
2,2t), or the group ring W[ℤ/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal
deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation. 相似文献
6.
Jeremy Yirmeyahu Kaminski Alexei Kanel-Belov Mina Teicher 《Journal of Mathematical Sciences》2008,149(2):1087-1097
Let X be an irreducible projective variety over an algebraically closed field of characteristic zero. For ≥ 3, if every (r−2)-plane
, where the x
i
are generic points, also meets X in a point x
r
different from x
1,..., x
r−1, then X is contained in a linear subspace L such that codim
L
X ≥ r − 2. In this paper, our purpose is to present another derivation of this result for r = 3 and then to introduce a generalization to nonequidimensional varieties. For the sake of clarity, we shall reformulate
our problem as follows. Let Z be an equidimensional variety (maybe singular and/or reducible) of dimension n, other than a linear space, embedded into ℙr, where r ≥ n + 1. The variety of trisecant lines of Z, say V
1,3(Z), has dimension strictly less than 2n, unless Z is included in an (n + 1)-dimensional linear space and has degree at least 3, in which case dim V
1,3(Z) = 2n. This also implies that if dim V
1,3(Z) = 2n, then Z can be embedded in ℙ
n + 1. Then we inquire the more general case, where Z is not required to be equidimensional. In that case, let Z be a possibly singular variety of dimension n, which may be neither irreducible nor equidimensional, embedded into ℙr, where r ≥ n + 1, and let Y be a proper subvariety of dimension k ≥ 1. Consider now S being a component of maximal dimension of the closure of
. We show that S has dimension strictly less than n + k, unless the union of lines in S has dimension n + 1, in which case dim S = n + k. In the latter case, if the dimension of the space is strictly greater than n + 1, then the union of lines in S cannot cover the whole space. This is the main result of our paper. We also introduce some examples showing that our bound
is strict.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 71–87, 2006. 相似文献
7.
Let U = ℂ2, Γ = ℤ2, and let ℂ[x
1±1, x
2±1] be the ring of Laurent polynomials. The Witt algebra L is the Lie algebra of derivations over ℂ[x
1±1, x
2±1], which is spanned by elements of the form D(u, r) = x
r
(u
1
d
1 + u
2
d
2), u = (u
1, u
2) ∈ U, r ∈ Γ, where d
1 and d
2 are the degree derivations of ℂ[x
1±1, x
2±1]. The image of gl
2-module V under Larsson functor F
α
, denoted by W = F
α
(V), gives a class of L-modules, often called the Larsson-modules of L. In this paper, we study the derivations from the Witt algebra L to its Larsson-modules W, and we determine the first cohomology group H
1(L,W). 相似文献
8.
Subordination of a killed Brownian motion in a bounded domain D⊂ℝ
d
via an α/2-stable subordinator gives a process Z
t
whose infinitesimal generator is −(−Δ|
D
)α/2, the fractional power of the negative Dirichlet Laplacian. In this paper we study the properties of the process Z
t
in a Lipschitz domain D by comparing the process with the rotationally invariant α-stable process killed upon exiting D. We show that these processes have comparable killing measures, prove the intrinsic ultracontractivity of the generator of
Z
t
, prove the intrinsic ultracontractivity of the semigroup of Z
t
, and, in the case when D is a bounded C
1,1
domain, obtain bounds on the Green function and the jumping kernel of Z
t
.
Received: 4 April 2002 / Revised version: 1 July 2002 / Published online: 19 December 2002
This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut
Oberwolfach. We thank the Institute for the hospitality.
The research of the first author is supported in part by NSF Grant DMS-9803240.
The research of the second author is supported in part by MZT grant 037008 of the Republic of Croatia.
Mathematics Subject Classification (2000): Primary 60J45; Secondary 60J75, 31C25
Key words or phrases: Killed Brownian motions – Stable processes – Subordination – Fractional Laplacian 相似文献
9.
We consider the asymptotic stability problems by Lyapunov functionals V for a class of functional differential equations with impulses of the form x′(t)=f(t,x
t
), x∈R
n
, t≧t
0, t≠t
k
; △x=I
k
(t,x(t
−)), t=t
k
, k∈Z
+
. Some new asymptotic stability results are presented by using an idea originated by Burton and Makay [6] and developed by
Zhang [1]. We generalize some known results about impulsive functional differential equations in the literature in which we
only require the derivative of V to be negative definite on a sequence of intervals I
n
=[s
n
,ξ
n
] which may or may not be contained in the sequence of impulsive time intervals [t
n
,t
n+1). 相似文献
10.
Abbas Salemi 《Mathematische Nachrichten》2000,217(1):141-146
Let T(λ, ε ) = λ2 + λC + λεD + K be a perturbed quadratic matrix polynomial, where C, D, and K are n × n hermitian matrices. Let λ0 be an eigenvalue of the unperturbed matrix polynomial T(λ, 0). With the falling part of the Newton diagram of det T(λ, ε), we find the number of differentiable eigenvalues. Some results are extended to the general case L(λ, ε) = λ2 + λD(ε) + K, where D(ε) is an analytic hermitian matrix function. We show that if K is negative definite on Ker L(λ0, 0), then every eigenvalue λ(ε) of L(λ, ε) near λ0 is analytic. 相似文献
11.
We study the Cauchy problem for the nonlinear dissipative equations (0.1) uo∂u-αδu + Β|u|2/n
u = 0,x ∃ Rn,t } 0,u(0,x) = u0(x),x ∃ Rn, where α,Β ∃ C, ℜα 0. We are interested in the dissipative case ℜα 0, and ℜδ(α,Β)≥ 0, θ = |∫ u0(x)dx| ⊋ 0, where δ(α, Β) = ##|α|n-1nn/2 / ((n + 1)|α|2 + α2
n/2. Furthermore, we assume that the initial data u0 ∃ Lp are such that (1 + |x|)αu0 ∃ L1, with sufficiently small norm ∃ = (1 + |x|)α u0 1 + u0 p, wherep 1, α ∃ (0,1). Then there exists a unique solution of the Cauchy problem (0.1)u(t, x) ∃ C ((0, ∞); L∞) ∩ C ([0, ∞); L1 ∩ Lp) satisfying the time decay estimates for allt0 u(t)||∞ Cɛt-n/2(1 + η log 〈t〉)-n/2, if hg = θ2/n 2π ℜδ(α, Β) 0; u(t)||∞ Cɛt-n/2(1 + Μ log 〈t〉)-n/4, if η = 0 and Μ = θ4/n 4π)2 (ℑδ(α, Β))2 ℜ((1 + 1/n) υ1-1 υ2) 0; and u(t)||∞ Cɛt-n/2(1 + κ log 〈t〉)-n/6, if η = 0, Μ = 0, κ 0, where υl,l = 1,2 are defined in (1.2), κ is a positive constant defined in (2.31). 相似文献
12.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
13.
E. V. Derets 《Ukrainian Mathematical Journal》2000,52(3):368-378
We establish lower bounds for the Kolmogorov widths d
2n-1(W
r
H
1ω.L
p
) and Gel’fand widths d
2n-1(W
r
H
1ω.L
p
) of the classes of functions W
r
H
1ω with a convex integral modulus of continuity ω(t). 相似文献
14.
15.
《代数通讯》2013,41(10):4765-4774
Abstract For vector spaces V and W over a field F, L F (V, W) denotes the set of all linear transformations α : V → W, and for a cardinal number k > 0, let L F (V, W, k) be the set of all α ∈ L F (V, W) of rank less than k. For θ ∈ L F (W, V), let (L F (V, W, k), θ) denote the semigroup L F (V, W, k) under the operation ? defined by α ? β = αθβ for all α, β ∈ L F (V, W, k). In this paper, all 0-minimal quasi-ideals of the semigroup (L F (V, W, k), θ) are completely characterized. It is also shown from this characterization that every nonzero semigroup (L F (V, W, k), θ) always has a 0-minimal quasi-ideal. 相似文献
16.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2009,61(7):1151-1157
The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings f ∈ W
1,n
loc such that their outer dilatation K
O
(x, f) belongs to L
n−1
loc and the measure of the set B
f
of branching points of f is equal to zero have finite length distortion. In other words, the images of almost all curves γ in the domain D under the considered mappings f : D → ℝ
n
, n ≥ 2, are locally rectifiable, f possesses the (N)-property with respect to length on γ, and, furthermore, the (N)-property also holds in the inverse direction for liftings of curves. The results obtained generalize the well-known Poletskii
lemma proved for quasiregular mappings. 相似文献
17.
F. A. Shamoyan 《Journal of Mathematical Sciences》2006,139(2):6491-6495
Let ϕ(r) = (ϕ1(r1), …, ϕn(rn)) be a vector-valued function on R
+
n
. A necessary and sufficient condition is obtained under which any function f ∈, H∞ (D
n
), f(z) ≠ 0, z ∈, D
n
, is cyclic in the corresponding weighted space Lp(ϕ), where D
n
is the unit polydisk in C
n. Bibliography: 13 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 226–234. 相似文献
18.
G. V. Radzievskii 《Ukrainian Mathematical Journal》2003,55(7):1218-1222
For the equation L
0
x(t) + L
1
x
(1)(t) + ... + L
n
x
(n)(t) = 0, where L
k, k = 0, 1, ... , n, are operators acting in a Banach space, we formulate conditions under which a solution x(t) that satisfies some nonlocal homogeneous boundary conditions is equal to zero. 相似文献
19.
V. P. Sklyarov 《Computational Mathematics and Mathematical Physics》2011,51(10):1679-1684
The behavior of the graph of the function Z
n
(t) = ∥Z
n
′(·, t)∥/∥Z
n
(·, t)∥ is discussed in the case where the functions Z
n
(x, t) are the Zolotarev polynomials and the norm is a weighted sup norm. Based on calculations performed for various weights,
it is conjectured that the characteristic jump in Z
n
(t) in the case of the Laguerre weight on a semiaxis is caused by the fact that the weight function is not symmetric about the
midpoint of the interval. 相似文献
20.
For a triple {V, H, V*} of Hilbert spaces, we consider an evolution inclusion of the form u′(t)+A(t)u(t)+δϕ(t, u(t)) ∋
f(t), u(0) = u0, t ∈ (0, T ], where A(t) and ϕ(t, ·), t ∈ [0, T], are a family of nonlinear operators from V to V * and a family of convex lower semicontinuous functionals with common effective domain D(ϕ) ⊂ V. We indicate conditions on the data under which there exists a unique solution of the problem in the space H
1(0, T; V)∩W
∞1 (0, T;H) and the implicit Euler method has first-order accuracy in the energy norm. 相似文献