共查询到20条相似文献,搜索用时 31 毫秒
1.
Evgueni Doubtsov 《Journal of Fourier Analysis and Applications》2006,12(3):225-231
Let μ be a measure on the complex sphere. Denote by μpq the projection of μ on H(p, q), the space of complex spherical harmonics. Assume that μpq = 0 if (p − 1)q ≠ 0, and ∥μ1q∥∞ → 0 as q → ∞. Then μ is absolutely continuous with respect to Lebesgue measure on the sphere. 相似文献
2.
A. A. Panov 《Mathematical Notes》1977,21(1):22-28
The number Kp,q, i.e., the number of (p, q) corridors of closed domains which are convex in the vertical direction, consist of elementary
squares of the integral lattice, are situated within a rectangle of the size q × p, and completely cover the side of length
p of this rectangle under projection is computed. The asymptotic (Kp,q/q2)1/p → λ, as p, q → ∞, where λ = 0.3644255… is the maximum root of the equation1F1(-1/2 − 1/(16λ), 1/2, 1/(4λ)) = 0,1F1 being the confluence hypergeometric function, is established. These results allow us to compute the ε entropy of the space
of continuous functions with the Hausdorff metric.
Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 39–50, January, 1977. 相似文献
3.
Let (K, μ) be a measurable space with μ(K)=1. Let Ip,q: Lp (K, μ)→Lq (K, μ) be the embedding operator. The Bernstein widths of Ip, q are considered. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 166–169.
Translated by S. V. Kislyakov. 相似文献
4.
Yinsheng Jiang Lin Tang 《分析论及其应用》2005,21(4):301-310
In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKα,p q(G) and HKq,p q(G), where 1 < q <∞, Q(1 - 1/q) ≤α<∞, 0 < p <∞ and G denotes a graded homogeneous Lie group. 相似文献
5.
V. A. Voblyi 《Mathematical Notes》1977,21(1):36-39
Let t(r, n) be the number of trees with n vertices of which r are hanging and q are internal (r=n−9). For a fixed r or q we
prove the validity of the asymptotic formulas (r > 2)t(r, n)≈t/r|(r−2)| 22−r
n
2r−4 (n→∞)t(n−q, n)≈1/q|(q−1)|q
q−2
n
q−1 (n→∞) In the derivation of these formulas we do not use the expression for the enumerator of the trees with respect to the number
of hanging vertices.
Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 65–70, January, 1977. 相似文献
6.
T. V. Dudnikova 《Theoretical and Mathematical Physics》2011,169(3):1668-1682
We study the dynamics of lattice systems in ℤd, d ≥ 1. We assume that the initial data are random functions. We introduce the family of initial measures {μ0ɛ, ɛ > 0}. The measures μ0ɛ are assumed to be locally homogeneous or “slowly changing” under spatial shifts of the order o(ɛ−1
) and inhomogeneous under shifts of the order ɛ−1
. Moreover, correlations of the measures μ0ɛ decrease uniformly in ɛ at large distances. For all τ ∈ ℝ \ 0, r ∈ ℝd, and κ > 0, we consider distributions of a random solution at the instants t = τ/ɛκ at points close to [r/ɛ] ∈ ℤd. Our main goal is to study the asymptotic behavior of these distributions as ɛ → 0 and to derive the limit hydrodynamic equations of the Euler and Navier-Stokes type. 相似文献
7.
Let X be a Banach space, A : D(A) X → X the generator of a compact C0- semigroup S(t) : X → X, t ≥ 0, D a locally closed subset in X, and f : (a, b) × X →X a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order to make D a viable domain of the semilinear differential equation of retarded type u'(t) = Au(t) + f(t, u(t - q)), t ∈ [to, to + T], with initial condition uto = φ ∈C([-q, 0]; X), is the tangency condition lim infh10 h^-1d(S(h)v(O)+hf(t, v(-q)); D) = 0 for almost every t ∈ (a, b) and every v ∈ C([-q, 0]; X) with v(0), v(-q)∈ D. 相似文献
8.
Evgeniy Pustylnik 《Journal d'Analyse Mathématique》1999,79(1):113-157
The Lorentz-Zygmund spaces, introduced by C. Bennett and K. Rudnick in [BR], are generalized by taking the exterior norm in
arbitrary rearrangement invariant spaceE instead of onlyL
r-spaces. On the spacesL
p,α,E thus obtained, we study all operatorsT of two weak types (a, b) and (p, q) with 1≤a<p≤∞, 1≤b<q≤∞, and prove thatT:L
p,α,E→L
q,α−1,E. Moreover, for any set of parametersp, q, α, E, we construct the smallest possible spaceB
q,α,E such thatT:L
p,α,E→B
q,α,E and the largest possible spaceA
p,α,E such thatT:A
p,α,E→L
q,α−1,E. For spaces of all three types, we find their fundamental functions and Boyd indices, state various embeddings, equivalences
and other properties.
The research was supported by the Center of Scientific Absorption of the Ministry of Absorption of the State of Israel. 相似文献
9.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
10.
LetX be a Banach space and leta, b, q be real numbers such thata<b,q>0. Denote byD a locally closed subset ofX. A necessary and sufficient condition for the existence of a mild solutionu∈C([a−q, b
1],X),a<b
1<b, to the differential equationdu(t)/dt=Au(t)+f(t, u
t), such thatu:[a,b
1]→D, u
a=ϕ is given. The linear operatorA is the generator of aC
0 semigroupT(t), t≧0, withT(t) compact fort>0,f: [a, b)×C([−q,0],D
λ)→X is continuous and ϕ∈C([−q,0],D
λ) with ϕ(0)∈D. D
λ is a neighbourhood ofD. Applications to parabolic partial differential equations with retarded argument are given. 相似文献
11.
Xueyan Xiang Qian He Wenshan Yang 《分析论及其应用》2007,23(3):243-254
Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn(., qn)} when n → ∞ and convergence rate of Bn(f,q;x) when f ∈ C^n-1 [0, 1], q → ∞ are also presented. 相似文献
12.
Liu Yongping 《分析论及其应用》1991,7(3):27-34
In this paper, we study the so-called entire (0,m1,m2,…mq)-interpolation on equidistant nodes for q=2r-1 case, obtain that it has unique solution B
rσ
2
,σ>0. if and only if E-O=−1, where E and O denote the number of even and odd integers in the {m1,…,mq} respectively, and give the explicit formulae of this kind of interpolation functions if they exist.
The Project Supported by National Natural Science Foundation of China 相似文献
13.
Meng Wang 《数学学报(英文版)》2012,28(1):145-170
We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition.In the previous paper,we show that the Chern-Simons Higgs equation with parameter λ0 has at least two solutions(uλ1,uλ2) for λ sufficiently large,which satisfy that uλ1→u0 almost everywhere as λ→∞,and that uλ2→∞ almost everywhere as λ→∞,where u 0 is a(negative) Green function on M.In this paper,we study the asymptotic behavior of the solutions as λ→∞,and prove that uλ2-uλ2 converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary M is negative,or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero. 相似文献
14.
Georg Schneider 《Czechoslovak Mathematical Journal》2005,55(4):947-956
We consider the solution operator S: ℱμ,(p,q) → L
2(μ)(p, q) to the
-operator restricted to forms with coefficients in ℱμ = {f: f is entire and ∫ℂn
|f(z)|2 dμ(z) < ∞}. Here ℱμ,(p,q) denotes (p,q)-forms with coefficients in ℱμ, L
2(μ) is the corresponding L
2-space and μ is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula
S to
. This solution operator will have the property Sv ⊥ ℱ(p,q) ∀v ∈ ℱ(p,q+1). As an application of the solution formula we will be able to characterize compactness of the solution operator in terms
of compactness of commutators of Toeplitz-operators
: ℱμ → L
2(μ). 相似文献
15.
Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type 总被引:17,自引:0,他引:17
W. A. Kirk 《Israel Journal of Mathematics》1974,17(4):339-346
LetX be a Banach space,K a nonempty, bounded, closed and convex subset ofX, and supposeT:K→K satisfies: for eachx∈K, lim sup
i→∞{sup
y∈K
‖t
ix−Tiy∼−‖x−y‖}≦0. IfT
N is continuous for some positive integerN, and if either (a)X is uniformly convex, or (b)K is compact, thenT has a fixed point inK. The former generalizes a theorem of Goebel and Kirk for asymptotically nonexpansive mappings. These are mappingsT:K→K satisfying, fori sufficiently large, ‖Tix−Tiy‖≦k
i‖x−y∼,x,y∈K, wherek
i→1 asi→∞. The precise assumption in (a) is somewhat weaker than uniform convexity, requiring only that Goebel’s characteristic of
convexity, ɛ0 (X), be less than one.
Research supported by National Science Foundation Grant GP 18045. 相似文献
16.
This paper, self-contained, deals with pseudo-unitary spin geometry. First, we present pseudo-unitary conformal structures
over a 2n-dimensional complex manifold V and the corresponding projective quadrics
for standard pseudo-hermitian spaces Hp,q. Then we develop a geometrical presentation of a compactification for pseudo-hermitian standard spaces in order to construct
the pseudo-unitary conformal group of Hp,q. We study the topology of the projective quadrics
and the “generators” of such projective quadrics. Then we define the space S of spinors canonically associated with the pseudo-hermitian scalar product of signature (2n−1, 2n−1). The spinorial group Spin U(p,q) is imbedded into SU(2n−1, 2n−1). At last, we study the natural imbeddings of the projective quadrics
相似文献
17.
Let S ⊂ ℜn+1
be the graph of the function ϕ :[−1, 1]
n → ℜ defined by ϕ (x
1
, …, xn) = ∑
j=1
n
|xj|αj, with1<α
1
≤ … ≤ αn, let σ the Euclidean area measure on S. In this article we study the Lp − Lq boundedness of convolution operators with the singular Borel measure on Rn+1
given by μ (E)=σ (E ∩ S) 相似文献
18.
The following Khintchine-type theorem is proved for manifoldsM embedded in ℝ
k
which satisfy some mild curvature conditions. The inequality |q·x| <Ψ(|q|) whereΨ(r) → 0 asr → ∞ has finitely or infinitely many solutionsqεℤ
k
for almost all (in induced measure) points x onM according as the sum Σ
r
= 1/∞
Ψ(r)r
k−2 converges or diverges (the divergent case requires a slightly stronger curvature condition than the convergent case). Also,
the Hausdorff dimension is obtained for the set (of induced measure 0) of point inM satisfying the inequality infinitely often whenψ(r) =r
−t
. τ >k − 1. 相似文献
19.
We consider the existence and uniqueness of singular solutions for equations of the formu
1=div(|Du|p−2
Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2.
Under a growth condition on ϕ(u) asu→∞, (H1), we prove that for everyc>0 there exists a singular solution such thatu(x, t)→cδ(x) ast→0. This solution is unique and is called a fundamental solution. Under additional conditions, (H2) and (H3), we show the
existence of very singular solutions, i.e. singular solutions such that ∫|x|≤r
u(x,t)dx→∞ ast→0. Finally, for functions ϕ which behave like a power for largeu we prove that the very singular solution is unique. This is our main result.
In the case ϕ(u)=u
q, 1≤q, there are fundamental solutions forq<p*=p-1+(p/N) and very singular solutions forp-1<q<p*. These ranges are optimal.
Dedicated to Professor Shmuel Agmon 相似文献
20.
K. L. Rychkov 《Journal of Applied and Industrial Mathematics》2011,5(2):290-295
A generalization of the concept of parallel-sequential switching circuits (π-circuits) to the case when the variables assigned to contacts can take not two, as in the Boolean case, but a greater number of values.
The conductivity of the contact is still two-valued (the contact is either closed or open). A lower bound is obtained on the
complexity of these circuits computing the q-ary counter of multiplicity q, i.e., the function φ
q
: {0, 1, …, q − 1}
n
→ {0, 1} that equals 1 if the sum of values of its variables is a multiple of q. 相似文献