共查询到20条相似文献,搜索用时 93 毫秒
1.
Feng Dai 《Journal of Mathematical Analysis and Applications》2006,315(2):711-724
We study the Kolmogorov m-widths and the linear m-widths of the weighted Besov classes on [−1,1], where Lq,μ, 1?q?∞, denotes the Lq space on [−1,1] with respect to the measure , μ>0. Optimal asymptotic orders of and as m→∞ are obtained for all 1?p,τ?∞. It turns out that in many cases, the orders of are significantly smaller than the corresponding orders of the best m-term approximation by ultraspherical polynomials, which is somewhat surprising. 相似文献
2.
Beth M. Campbell Hetrick Rhonda J. Hughes 《Journal of Mathematical Analysis and Applications》2007,331(1):342-357
We apply semigroup theory and other operator-theoretic methods to prove Hölder-continuous dependence on modeling for the inhomogeneous ill-posed Cauchy problem in Banach space. The inhomogeneous ill-posed Cauchy problem is given by , u(0)=χ, 0?t<T; where −A is the infinitesimal generator of a holomorphic semigroup on a Banach space X, χ∈X, and . For a suitable function f, the approximate problem is given by , v(0)=χ. Under certain stabilizing conditions, we prove that for a related norm, where and M are computable constants independent of β, 0<β<1, and ω(t) is a harmonic function. These results extend earlier work of Ames and Hughes on the homogeneous ill-posed problem. 相似文献
3.
Tian-Xiao Pang Zheng-Yan Lin 《Journal of Mathematical Analysis and Applications》2007,334(2):1246-1259
Let be a sequence of independent and identically distributed positive random variables, which is in the domain of attraction of the normal law, and tn be a positive, integer random variable. Denote , , where denotes the sample mean. Then we show that the self-normalized random product of the partial sums, , is still asymptotically lognormal under a suitable condition about tn. 相似文献
4.
Liangping Jiang 《Journal of Mathematical Analysis and Applications》2005,301(2):378-383
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a positive definite function V which has infinitesimal upper bound such that is negative definite. In this paper we prove that if is bounded then the condition that is negative definite can be weakened and replaced by that and is negative definite. 相似文献
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Gen-Qi Xu 《Journal of Mathematical Analysis and Applications》2004,289(2):493-504
The eventually norm continuous semigroups on Hilbert space and perturbation are studied in this paper. By resolvent of infinitesimal generator, the sufficient and necessary conditions for eventually norm continuous semigroups are given. Using the result obtained, it is proved that if is infinitesimal generator of an eventually norm continuous semigroup T(t), then there is a subspace ΞA of such that, for any , the semigroup S(t) generated by preserves the property of T(t). 相似文献
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The well-posedness of the Cauchy problem to the generalized Korteweg-de Vries-Benjamin-Ono equation is considered. Local results for data in (s?−1/8) and the global well-posedness for data in are obtained if l=2. Moreover, for l=3, the problem is locally well-posed for data in Hs (s?1/4). The main idea is to use the Fourier restriction norm method. 相似文献
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On the number of positive solutions of nonlinear systems 总被引:1,自引:0,他引:1
Haiyan Wang 《Journal of Mathematical Analysis and Applications》2003,281(1):287-306
We prove that appropriate combinations of superlinearity and sublinearity of with respect to at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system 0<t<1. The vector-valued function is defined by where and ? covers the two important cases ?(u′)=u′ and ?(u′)=|u′|p−2u′, p>1. Our methods employ fixed point theorems in a cone. 相似文献
8.
Tomoyoshi Ohwada Guoxing Ji Atsushi Hasegawa 《Journal of Mathematical Analysis and Applications》2006,315(1):216-224
Let G be a compact abelian group with the totally ordered dual group which admits the positive semigroup . Let N be a von Neumann algebra and be an automorphism group of on N. We denote to the analytic crossed product determined by N and α. We show that if is a maximal σ-weakly closed subalgebra of , then induces an archimedean order in . 相似文献
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Emin Özça? ?nci Ege Ha?met Gürçay 《Journal of Mathematical Analysis and Applications》2007,326(1):101-107
The distributions and were defined as the neutrix limit of the sequences and respectively for , see [J.D. Nicholos, B. Fisher, The distribution composition , J. Math. Anal. Appl. 258 (2001) 131-145; B. Fisher, On defining the distribution , Univ. u Novom Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 15 (1985) 119-129]. We here consider these distributions when r=0. In other words, we define the sth powers of the Heaviside function H(x) in the distributional sense for negative integers. Further compositions are also considered. 相似文献
11.
G. Metafune 《Journal of Mathematical Analysis and Applications》2004,294(2):596-613
We deal with Markov semigroups Tt corresponding to second order elliptic operators Au=Δu+〈Du,F〉, where F is an unbounded locally Lipschitz vector field on . We obtain new conditions on F under which Tt is not analytic in . In particular, we prove that the one-dimensional operator Au=u″−x3u′, with domain , , is not sectorial in . Under suitable hypotheses on the growth of F, we introduce a class of non-analytic Markov semigroups in , where μ is an invariant measure for Tt. 相似文献
12.
Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
13.
Saroj Kumar Dash 《Journal of Mathematical Analysis and Applications》2008,339(1):98-107
For a symmetric stable process X(t,ω) with index α∈(1,2], f∈Lp[0,2π], p?α, and , we establish that the random Fourier-Stieltjes (RFS) series converges in the mean to the stochastic integral , where fβ is the fractional integral of order β of the function f for . Further it is proved that the RFS series is Abel summable to . Also we define fractional derivative of the sum of order β for an, An(ω) as above and . We have shown that the formal fractional derivative of the series of order β exists in the sense of mean. 相似文献
14.
Let , B and Aj () be real nonsingular n×n matrices, λk () be real numbers. In this paper we present a sufficient condition for the system to be a frame for . This sufficient condition also shows the stability of the system with respect to the perturbation of matrix dilation parameters and the perturbation of translation parameters . 相似文献
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On commutators of Marcinkiewicz integrals with rough kernel 总被引:2,自引:0,他引:2
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Let be the polynomial whose zeros are the j-invariants of supersingular elliptic curves over . Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier (Computational Perspectives on Number Theory (Chicago, IL, 1995), AMS/IP 7 (1998) 97-126), we define an inner product on for every . Suppose a system of orthogonal polynomials {Pn,ψ(x)}n=0∞ with respect to exists. We prove that if n is sufficiently large and ψ(x)Pn,ψ(x) is p-integral, then over . Further, we obtain an interpretation of these orthogonal polynomials as a p-adic limit of polynomials associated to p-adic modular forms. 相似文献
20.
Wolfgang Knirsch Georg Schneider 《Journal of Mathematical Analysis and Applications》2006,320(1):403-414
In this paper we investigate Hankel operators with anti-holomorphic symbols ∈L2(C,m|z|), where are general Fock spaces. We will show that is not continuous if the corresponding symbol is not a polynomial . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials we will give a complete characterization of the Schatten-von Neumann p-class membership for p>0. Namely in case 2k<m the Hankel operators are in the Schatten-von Neumann p-class iff p>2m/(m−2k); and in case 2k?m they are not in the Schatten-von Neumann p-class. 相似文献