共查询到20条相似文献,搜索用时 687 毫秒
1.
ShuJunDANG LiZhongPENG 《数学学报(英文版)》2004,20(2):255-260
This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators Tn:L^2(R)→L^2(C,e^-|z|^2/2dzd-↑z/4πi), s.t. TnL^2(R) lontain in L^2(C,e^-|z|^2/2dzd-↑z/4πi) are reproducing subspaces (n=0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of TnL^2(R), Furthermore, it shows the orthogonal spaces decomposition of L^2(C,e^-|z|^2/2dzd-↑z/4πi). Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6]. 相似文献
2.
In this paper, we prove that
and round geodesic spheres are the only n-dimensional compact embedded rotation hypersurfaces with Hm = 0 (1 ≤ m ≤ n − 1) in a unit sphere Sn+1(1). When m = 1, our result reduces to the result of T. Otsuki [O1], [O2], Brito and Leite [BL].
The project is supported by the grant No. 10531090 of NSFC. 相似文献
3.
Xiu Min REN Kai Man TSANG 《数学学报(英文版)》2007,23(2):265-280
In this paper, it is proved that with at most O(N65/66) exceptions, all even positive integers up to N are expressible in the form p^2 2+p^3 3+p^4 4+p^5 5. This improves a recent result O(N19193/19200+ε) due to C. Bauer. 相似文献
4.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
5.
Xi Mei WU Qin YUE 《数学学报(英文版)》2007,23(11):2061-2068
Let F = Q(√-p1p2) be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol (p1/p2) = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold: (1) The quartic residue symbols (p1/p2)4 = (p2/p1)4 = 1; (2) Either both
p1 and p2 are represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=ε(2x^2-p1y^2),x,y∈Z,ε∈{±1},where h+(2p1) is the narrow class number of Q(√2p1),Moreover, we also generalize these results. 相似文献
6.
Yu Xiang LI 《数学学报(英文版)》2006,22(2):545-550
We will show in this paper that if A is very close to 1, then
I(M,λ,m) =supu∈H0^1,n(m),∫m|△↓u|^ndV=1∫Ω(e^αn|u|^n/(n-1)-λm∑k=1|αnun/(n-1)|k/k!)dV
can be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" (Comm. Pure. Appl. Math., 55, 135-152, 2002). 相似文献
7.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
8.
A Note on Certain Block Spaces on the Unit Sphere 总被引:1,自引:0,他引:1
Xiao Feng YE Xiang Rong ZHU 《数学学报(英文版)》2006,22(6):1843-1846
In this note, we clarify a relation between block spaces and the Hardy space. We obtain Bq^0.v belong to H^1(S^n-1)+L(ln+L)^1+v(s^n-1),v〉-1,q〉1,Furthermore,if v≥ 0, q 〉 1. we verify that block spaces Rq^0.v(S^n-1)are proper subspaces of H1 (S^n- 1), 相似文献
9.
Multilinear Singular Integrals with Rough Kernel 总被引:9,自引:0,他引:9
ShanZhenLU HuoXiongWU PuZHANG 《数学学报(英文版)》2003,19(1):51-62
For a class of multilinear singular integral operators T
A
,
where R
m
(A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m − 1 in
is homogeneous of degree zero, the authors prove that T
A
is bounded from L
p
(ℝ
n
) to
and from L
1(ℝ
n
) to L
n/(n−β),∞(ℝ
n
) with the bound
And if Ω has vanishing moments of order m − 1 and satisfies some kinds of Dini regularity otherwise, then T
A
is also bounded from L
p
(ℝ
n
) to
with the bound
Supported by the National 973 Project (G1990751) and SEDF of China (20010027002) 相似文献
10.
Let f be in the localized nonisotropic Sobolev space
on the n-dimensional
Heisenberg group ℍ
n
= ℂ
n
× ℝ, where 1 = p < Q and Q = 2n + 2 is the homogeneous dimension
of ℍn. Suppose that the subelliptic gradient is gloablly L
p
integrable, i.e.,
is finite.
We prove a Poincaré inequality for f on the entire space ℍ
n
. Using this inequality we prove that the
function f subtracting a certain constant is in the nonisotropic Sobolev space formed by the completion
of
under the norm of
We will also prove that the best constants and extremals for such Poincaré inequalities on ℍ
n
are
the same as those for Sobolev inequalities on ℍ
n
. Using the results of Jerison and Lee on the sharp
constant and extremals for L
2 to
Sobolev inequality on the Heisenberg group, we thus arrive
at the explicit best constant for the aforementioned Poincaré inequality on ℍ
n
when p = 2. We also
derive the lower bound of the best constants for local Poincaré inequalities over metric balls on the
Heisenberg group ℍ
n
.
The first author is supported by Zhongdian grant of NSFC; The second author is supported by a global grant at Wayne State
University and by NSF of USA 相似文献
11.
S. BERHANU F. CUCCU G. PORRU 《数学学报(英文版)》2007,23(3):479-486
For γ≥1 we consider the solution u=u(x) of the Dirichlet boundary value problem Δu + u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate
u(x)=p(δ(x))[1+A(x)(log 1/δ(x)^-6],
where p(r) ≈ r r√2 log(1/r) near r = 0,δ(x) denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A(x) is a bounded function. For 1 〈 γ 〈 3 we find
u(x)=(γ+1/√2(γ-1)δ(x))^2/γ+[1+A(x)(δ(x))2γ-1/γ+1]
For γ3= we prove that
u(x)=(2δ(x))^1/2[1+A(x)δ(x)log 1/δ(x)] 相似文献
12.
GuiQiaoXU YongPingLIU 《数学学报(英文版)》2004,20(1):81-92
This paper concerns the problem of average σ-width of Sobolev-Wiener classes W^rpq(R^d),W^rpq(M,R^d),and Besov-Wiener classes S^rpqθb(R^d).S^rpqθB(R^d),S^rpqθb(M,R^d),S^rpqθB(R^d)in the metric Lq(R^d) for 1≤q≤p≤∞.The weak asymptotic results concerning the average linear widths,the average Bernstein widths and the infinite-dimensional Gel‘fand widths are obtained,respectively. 相似文献
13.
Dong Sheng Kang 《数学学报(英文版)》2009,25(3):435-444
Suppose Ω belong to R^N(N≥3) is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ:=((N-1)/2)^2,0≤μi〈(√μ-ai)^2,ai〈bi〈ai+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k(-div(|x-ξi|^-2ai△↓u)-μiu/|x-ξi|^2(1+ai)-u^pi-1/|x-ξi|^bipi)=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k. 相似文献
14.
Huaning Liu 《Bulletin of the Brazilian Mathematical Society》2007,38(2):179-188
For integers a,
b and n
> 0, define
and
where
denotes the summation over all
r such that (r, n) = 1, and
is defined by the equation
. The two sums are analogous to the
homogeneous Dedekind sum S(a,b,
n). The functional equations for
A
Γ and B
Γ are established. Furthermore, Knopp's
identity on Dedekind sum is extended.
*This work is supported by the N.S.F. (10271093,
60472068) of P.R. China. 相似文献
15.
Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
16.
Vito Lampret 《Central European Journal of Mathematics》2010,8(3):488-499
Zeta-generalized-Euler-constant functions,
$
\gamma \left( s \right): = \sum\limits_{k = 1}^\infty {\left( {\frac{1}
{{k^s }} - \int_k^{k + 1} {\frac{{dx}}
{{x^s }}} } \right)}
$
\gamma \left( s \right): = \sum\limits_{k = 1}^\infty {\left( {\frac{1}
{{k^s }} - \int_k^{k + 1} {\frac{{dx}}
{{x^s }}} } \right)}
相似文献
17.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
18.
Qi Kang RAN 《数学学报(英文版)》2005,21(4):705-714
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function. 相似文献
19.
De Li LI Andrew ROSALSKY Andrei VOLODIN 《数学学报(英文版)》2007,23(4):599-612
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
(i) lim sup n→∞ ||Sn||/an〈∞ a.s.and
∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent;
(ii) For all constants λ ∈ [0, ∞),
lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
20.
Kil-Woung JUN Hark-Mahn KIM 《数学学报(英文版)》2006,22(6):1781-1788
In this paper, we establish the general solution and the generalized Hyers-Ulam-Rassias stability problem for a cubic Jensen-type functional equation,4f((3x+y)/4)+4f((x+3y)/4)=6f((x+y)/2)+f(x)+f(y),9f((2x+y/3)+9f((x+2y)/3)=16f((x+y)/2+f(x)+f(y)in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gaevruta. 相似文献
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