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1.
We find the exact asymptotics (asn→∞) of the bestL
1-approximations of classesW
1
r
of periodic functions by spliness∈S
2n, r∼-1
(S
2n, r∼-1
is a set of 2π-periodic polynomial splines of orderr−1, defect one, and with nodes at the pointskπ/n,k∈ℤ) such that V
0
2π
s(
r-1)≤1+ɛ
n
, where {ɛ
n
}
n=1
∞
is a decreasing sequence of positive numbers such that ɛ
n
n
2→∞ and ɛ
n
→0 asn→∞.
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 435–444,
April, 1999. 相似文献
2.
M. Abad J. P. Díaz Varela B. F. López Martinolich M. del C. Vannicola M. Zander 《Central European Journal of Mathematics》2006,4(4):547-561
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L
p,k, and the finite field F(p
k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L
p,k) generated by L
p,k into the variety V(F(p
k)) generated by F(p
k) and an interpretation Φ2 of V(F(p
k)) into V(L
p,k) such that Φ2Φ1(B) = B for every B ε V(L
p,k) and Φ1Φ2(R) = R for every R ε V(F(p
k)). 相似文献
3.
Kunyu Guo 《Arkiv f?r Matematik》2000,38(1):97-110
For an essentially normal operatorT, it is shown that there exists a unilateral shift of multiplicitym inC
*
(T) if and only if γ(T)≠0 and γ(T)/m. As application, we prove that the essential commutant of a unilateral shift and that of a bilateral shift are not isomorphic
asC
*
-algebras. Finally, we construct a naturalC
*
-algebra ε + ε* on the Bergman spaceL
a
2
(B
n
), and show that its essential commutant is generated by Toeplitz operators with symmetric continuous symbols and all compact
operators.
Supported by NSFC and Laboratory of Mathematics for Nonlinear Science at Fudan University. 相似文献
4.
V. F. Gaposhkin 《Mathematical Notes》1998,64(3):316-321
The asymptotic behavior asn → ∞ of the normed sumsσn =n
−1 Σ
k
=0n−1
Xk for a stationary processX = (X
n
,n ∈ ℤ) is studied. For a fixedε > 0, upper estimates for P(sup
k≥n
|σ
k
| ≥ε) asn → ∞ are obtained.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 366–372, September, 1998. 相似文献
5.
We prove dimension free L
∞ → L
∞-estimates for the Riesz transform T = V L
−1, L = −Δ + V, where Δ is the Laplacian in ℝ
d
, and the polynomial V ≥ 0 satisfies C. L. Fefferman conditions; see [7]. As a corollary we get dimension free L
p
→ L
p(ℓ
2)-estimates, 1 < p < ∞, for the vector of Riesz transforms. 相似文献
6.
Sergio Campanato 《Annali dell'Universita di Ferrara》1977,23(1):169-187
Riassunto Nel cilindroQ=Ω×(0,T) si considerano sistemi parabolici (E+ϖ/ϖt) di forma non variazionale e con coefficienti discontinui, e si dimostra un teorema di isomorfismoW
0
p
(Q)→L
p
(Q;R
N
) e un teorema di regolarità locale negli spazi di Morrey.
Lavoro eseguito nell’ambito del gruppo G.N.A.F.A. del C.N.R. 相似文献
Summary In the cylinderQ=Ω×(0, T) we consider parabolic systems (E+ϖ/ϖt), in non variational form and with discontinuous coefficients, and we prove an theorem of isomorphismW 0 p (Q)→L p (Q;R N ) and an theorem of local regularity in the Morrey’s spaces.
Lavoro eseguito nell’ambito del gruppo G.N.A.F.A. del C.N.R. 相似文献
7.
LetX be a Banach space and letA be the infinitesimal generator of a differentiable semigroup {T(t) |t ≥ 0}, i.e. aC
0-semigroup such thatt ↦T(t)x is differentiable on (0, ∞) for everyx εX. LetB be a bounded linear operator onX and let {S(t) |t ≥ 0} be the semigroup generated byA +B. Renardy recently gave an example which shows that {S(t) |t ≥ 0} need not be differentiable. In this paper we give a condition on the growth of ‖T′(t)‖ ast ↓ 0 which is sufficient to ensure that {S(t) |t ≥ 0} is differentiable. Moreover, we use Renardy’s example to study the optimality of our growth condition. Our results can
be summarized roughly as follows:
We also show that if lim sup
t→0+t
p ‖T′(t)‖<∞ for a givenp ε [1, ∞), then lim sup
t→0+t
p‖S′(t)‖<∞; it was known previously that if limsup
t→0+t
p‖T′(t)‖<∞, then {S(t) |t ≥ 0} is differentiable and limsup
t→0+t
2p–1‖S′(t)‖<∞. 相似文献
(i) | If lim sup t→0+t log‖T′(t)‖/log(1/2) = 0 then {S(t) |t ≥ 0} is differentiable. |
(ii) | If 0<L=lim sup t→0+t log‖T′(t)‖/log(1/2)<∞ thent ↦S(t ) is differentiable on (L, ∞) in the uniform operator topology, but need not be differentiable near zero |
(iii) | For each function α: (0, 1) → (0, ∞) with α(t)/log(1/t) → ∞ ast ↓ 0, Renardy’s example can be adjusted so that limsup t→0+t log‖T′(t)‖/α(t) = 0 andt →S(t) is nowhere differentiable on (0, ∞). |
8.
Alexander Šostak 《Journal of Mathematical Sciences》2007,144(5):4527-4534
Given an M-valued equality E: X×X → M on a set X, we extend it to the M-valued equality ε: L
X
× L
X
→ M on the L-powerset L
X
of X, where L is a complete sublattice of a GL-monoid M. As a result, we come to a category SET(M,L) whose objects are quadruples (X,E,L
X
, ε). This category serves as a ground category for the category L-TOP(M) of (L,M)-valued topological spaces and some of its subcategories, which are the main subject of this paper. In particular, as special
cases, we obtain here Chang-Goguen, Lowen, Kubiak-Šostak, and some other known categories related to fuzzy topology.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 237–247, 2005. 相似文献
9.
Miloš Zlámal 《Annali di Matematica Pura ed Applicata》1962,57(1):143-150
Summary We consider the Dirichlet problem for the equation Lε(u) ≡ uxx+ɛuyy++A(x, y)ux−B(y)uy+C(x, y)u=F(x, y) where B(y)>0 and ɛ is a small positive parameter. An asymptotic formula is proved, from which it follows
that in a suitable part of the domain of definition u(x, y, ɛ)→U(x, y) as ɛ→0+, where U(x, y) is the solution of the corresponding
boundary - value problem for the reduced equation L0(U)≡Uxx+A(x, y)Ux−B(y)U+C(x, y)U=F(x, y).
To Enrico Bompiani on his scientific Jubilee. 相似文献
10.
I. Kh. Khusnullin 《Computational Mathematics and Mathematical Physics》2010,50(4):646-664
A perturbed two-parameter boundary value problem is considered for a second-order differential operator on an interval with
Dirichlet conditions. The perturbation is described by the potential μ−1
V((x − x
0)ɛ−1), where 0 < ɛ ≪ 1 and μ is an arbitrary parameter such that there exists δ > 0 for which ɛ/μ = o(ɛδ). It is shown that the eigenvalues of this operator converge, as ɛ → 0, to the eigenvalues of the operator with no potential.
Complete asymptotic expansions of the eigenvalues and eigenfunctions of the perturbed operator are constructed. 相似文献
11.
Summary Let Lεu and L
0
v be the elliptic and “backward” heat operators defined by(1.1) and(1.2), respectively. The following question is considered for a pair of “non-well posed” initial-boundary value problems for Lε and L
0
: if u and v are the respective solutions, under what restrictions on the classes of admissible solutions and in what sense,
if any, does u converge to v as ɛ →0?
This research was supported in part by the National Science Foundation Grant No. GP 5882 with Cornell University. 相似文献
12.
We investigate boundedness of the evolutione
itH in the sense ofL
2(ℝ3→L
2(ℝ3) as well asL
1(ℝ3→L
∞(ℝ3) for the non-selfadjoint operator
where μ>0 andV
1, V2 are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation around a standing wave,
and the aforementioned bounds are needed in the study of nonlinear asymptotic stability of such standing waves. We derive
our results under some natural spectral assumptions (corresponding to a ground state soliton of NLS), see A1)–A4) below, but
without imposing any restrictions on the edges±μ of the essential spectrum. Our goal is to develop an “axiomatic approach,”
which frees the linear theory from any nonlinear context in which it may have arisen.
This work was initiated in June of 2004, while the first author visited Caltech, and he wishes to thank that institution for
its hospitality and support. The first author was partially supported by the NSF grant DMS-0303413. The second author was
partially supported by a Sloan fellowship and the NSF grant DMS-0300081. The authors thank Avy Soffer for his interest in
this work. 相似文献
13.
Résumé Soit X un processus gaussien stationnaire non dérivable. Nous étudions le nombre de passages en zéro du processus régularisé par
convolution. Sous des hypothèses peu restrictives sur X, cette variable convenablement normalisée, converge au sens de L
2 quand la taille du filtre tend vers zéro. Lorsque X admet un temps local continu, la limite obtenue est le temps local.
Summary Let {X(t)} be a stationary non differentiable Gaussian process and let ϕɛ(u=ɛ−1 ϕ(u/ɛ) be an approximate identity. Setting X ɛ(t)=X*ϕɛ(t) and letting N ɛ(T) be the number of zeros of X ɛ in the interval [0, T] it is shown that under weak technical conditions there are constants C(ɛ) so that C(ɛ) N ɛ(T) converges in L 2 as ɛ→0. When X admits a continuous local time, the limit is the local time L(0, T) at zero of X(t).相似文献
14.
V. V. Yablokov 《Journal of Mathematical Sciences》2006,135(1):2803-2811
The problem of homogenization is considered for the solutions of the Neumann problem for the Lamé system of plane elasticity
in two-dimensional domains with channels that have the form of rectilinear cylinders of length ε
q (ε is a small positive parameter, q = const > 0) and radius a
ɛ. The bases of the channels form an ε-periodic structure on the hyperplane {x ∈ ℝ2: x
1 = 0} and their number is equal to N
ɛ= O(ɛ−1) as ε → 0. Under the limit condition lim
on the parameters characterizing the geometry of the domain, the weak H
1-limit of the generalized solution of this problem is found.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 310–322, 2005. 相似文献
15.
Nimish A. Shah 《Proceedings Mathematical Sciences》1996,106(2):105-125
LetL be a Lie group and λ a lattice inL. SupposeG is a non-compact simple Lie group realized as a Lie subgroup ofL and
. LetaεG be such that Ada is semisimple and not contained in a compact subgroup of Aut(Lie(G)). Consider the expanding horospherical subgroup ofG associated toa defined as U+ ={gεG:a
−n gan} →e as
n → ∞. Let Ω be a non-empty open subset ofU
+ andn
i
→ ∞ be any sequence. It is showed that
. A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result,
we describeG-equivariant topological factors of L/gl × G/P, where the real rank ofG is greater than 1,P is a parabolic subgroup ofG andG acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces
of Lie groups. 相似文献
16.
Jiahong Wu 《Journal d'Analyse Mathématique》1997,73(1):251-265
In this paper we study the classical problem in turbulence for the magneto-hydrodynamics (MHD) equations: whether the solutions
(u
(v),B
(v)) of the viscous MHD equations tend to the solutions (u
(0),B
(v)) of the inviscid MHD equations as the Reynolds numbersRe, Rm → ∞. As a preparation we first derive bounds for ||(u
(0),B
(0)(t)||H
m) (m ≥3) in terms of deformation tensor related quantities (0.1) {ie251-1} We then show that asRe → ∞ andRm → ∞, the difference {ie-251-2} {ie-251-3} converges to zero uniformly int as long as the quantities in (0.1) remain finite. The convergence rates are explicit.
Supported by the NSF grant DMS 9304580 at IAS. 相似文献
17.
Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献
18.
Wolfgang Wasow 《Commentarii Mathematici Helvetici》1971,46(1):65-86
A system of linear differential equations of the vectorial form εdy/dx=A (x, ε) y is considered, where ε is a positive parameter, and the matrixA (x, ε) is holomorphic in |x|⩽x
0, 0 < ε ⩽ ε0 , with an asymptotic expansionsA (x, ε) ∼ ∑
r=0
∞
A
r
(x) ε
r
, as ε→0. The eigenvalues ofA
0(x) are supposed to coalesce atx=0 so as to make this point a simple turning point. With the help of refinements of the representations for the inner and
outer asymptotic solutions, as ε→0, that were introduced in the articles [9] and [10] by the author (see the references at
the end of the paper), explicit connection formulas between these solutions are calculated. As part of this derivation it
is shown that only the diagonal entries of the connection matrix are asymptotically relevant. 相似文献
19.
This note contains the first example of a 1-parameter semigroup {T
pt≧0} of linear contractions inL
p (1<p<∞) for which the assertion of the local ergodic theorem (t
1∝0′T
sfds conv. a.e. ast → 0+0 for allf ∈L
p) fails to be true. The first example is a continuous semigroup of unitary operators inL
2, the second a power-bounded continuous semigroup of positive operators inL
1. This answers problems of Kubokawa, Fong and Sucheston.
In memory of our friend and colleague Shlomo Horowitz 相似文献
20.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献