共查询到20条相似文献,搜索用时 15 毫秒
1.
V. Maier 《Analysis Mathematica》1978,4(4):289-295
Оператор Канторович а дляf∈L p(I), I=[0,1], определяе тся соотношением $$P_n (f,x) = (n + 1)\sum\limits_{k = 0}^n {\left( {\begin{array}{*{20}c} n \\ k \\ \end{array} } \right)} x^k (1 - x)^{n - 1} \int\limits_{I_k } {f(t)dt,} $$ гдеI k=[k/(n}+1),(k+1)/(n+ 1)],n∈N. Доказывается, что есл ир>1 иf∈W p 2 (I), т.е.f абсол ютно непрерывна наI иf″∈L p(I), то $$\left\| {P_n f - f} \right\|_p = O(n^{ - 1} ).$$ Далее, установлено, чт о еслиf∈L p(I),p>1 и ∥P n f-f∥р=О(n ?1), тоf∈S, гдеS={f∶f аб-солютно непрерывна наI, x(1?x)f′(x)=∝ 0 x h(t)dt, гдеh∈L p(I) и ∝ 0 1 h(t)dt=0}. Если жеf∈Lp(I),p>1, то из условия ∥P n(f)?f∥pL=o(n?1) вытекает, чтоf постоянна почти всюду. 相似文献
2.
The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (-Δ) -α/2 are extended to the generalised fractional integrals L-α/2 for 0 < α < n, where L =-div A is a uniformly complex elliptic operator with bounded measurable coefficients in Rn. 相似文献
3.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
4.
Giuseppe Chiti 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1982,33(1):143-148
Summary An integral inequality for the eigenfunctions of linear second order elliptic operators in divergence form is proved. The result is a generalization of the Payner-Rayner inequality.
This study was performed within the G.N.A.F.A. of the Italian C.N.R. 相似文献
Résumé On démontre une inégalité intégrale pour les fonctions propres d'une classe d'opérateurs linéaires élliptiques du deuxième ordre. Le résultat est une généralization de l'inégalité de Payner-Rayner.
This study was performed within the G.N.A.F.A. of the Italian C.N.R. 相似文献
5.
Sarika Goyal K. Sreenadh 《NoDEA : Nonlinear Differential Equations and Applications》2014,21(4):567-588
In this article, we study the Fu?ik spectrum of the fractional Laplace operator which is defined as the set of all \({(\alpha, \beta)\in \mathbb{R}^2}\) such that $$\quad \left.\begin{array}{ll}\quad (-\Delta)^s u = \alpha u^{+} - \beta u^{-} \quad {\rm in}\;\Omega \\ \quad \quad \quad u = 0 \quad \quad \quad \qquad {\rm in}\; \mathbb{R}^n{\setminus}\Omega.\end{array}\right\}$$ has a non-trivial solution u, where \({\Omega}\) is a bounded domain in \({\mathbb{R}^n}\) with Lipschitz boundary, n > 2s, \({s \in (0, 1)}\) . The existence of a first nontrivial curve \({\mathcal{C}}\) of this spectrum, some properties of this curve \({\mathcal{C}}\) , e.g. Lipschitz continuous, strictly decreasing and asymptotic behavior are studied in this article. A variational characterization of second eigenvalue of the fractional eigenvalue problem is also obtained. At the end, we study a nonresonance problem with respect to the Fu?ik spectrum. 相似文献
6.
7.
Sourav Chatterjee 《Probability Theory and Related Fields》2009,143(1-2):1-40
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments. In the process, we introduce a notion of ‘second order Poincaré inequalities’: just as ordinary Poincaré inequalities give variance bounds, second order Poincaré inequalities give central limit theorems. The proof of the main result employs Stein’s method of normal approximation. A number of examples are worked out, some of which are new. One of the new results is a CLT for the spectrum of gaussian Toeplitz matrices. 相似文献
8.
V. E. Adler 《Functional Analysis and Its Applications》2016,50(4):257-267
We solve the classification problem for integrable lattices of the form u, t = f(u ?2,..., u 2) under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains five equations, including three new ones. Difference Miura-type substitutions are found, which relate these equations to known polynomial lattices. We also present some classification results for generic lattices. 相似文献
9.
10.
We develop a theory of second order diffusion processes and associated stochastic differential equations of second order. We show that equations of evolution of the density, mean velocity and momentum flux are a family of first order conservation laws similar to those of continuum mechanics. We verify that the theory is satisfied for a large class of reciprocal Gaussian processes 相似文献
11.
Kwang Ho SHON 《中国科学A辑(英文版)》2007,50(6):786-800
In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart. 相似文献
12.
Given an open domain (possibly unbounded) Ω?R n , we prove that uniformly elliptic second order differential operators, under nontangential boundary conditions, generate analytic semigroups in L 1(Ω). We use a duality method, and, further, give estimates of first order derivatives for the resolvent and the semigroup, through properties of the generator in Sobolev spaces of negative order. 相似文献
13.
14.
Mieko Tanaka 《Calculus of Variations and Partial Differential Equations》2014,51(1-2):87-115
By variational methods and Morse theory, we prove the existence of uncountably many \((\alpha ,\beta )\in \mathbb R ^2\) for which the equation \(-\mathrm{div}\, A(x, \nabla u)=\alpha u_+^{p-1} -\beta u_-^{p-1}\) in \(\Omega \) , has a sign changing solution under the Neumann boundary condition, where a map \(A\) from \(\overline{\Omega }\times \mathbb R ^N\) to \(\mathbb R ^N\) satisfying certain regularity conditions. As a special case, the above equation contains the \(p\) -Laplace equation. However, the operator \(A\) is not supposed to be \((p-1)\) -homogeneous in the second variable. In particular, it is shown that generally the Fu?ík spectrum of the operator \(-\mathrm{div}\, A(x, \nabla u)\) on \(W^{1,p}(\Omega )\) contains some open unbounded subset of \(\mathbb R ^2\) . 相似文献
15.
16.
A new class of estimators of a “scale” second order parameter 总被引:1,自引:0,他引:1
For a large class of heavy-tailed distribution functions F in the domain of attraction for maxima of an Extreme Value distribution with tail index γ>0, the function A(t), controlling the speed of convergence of maximum values, linearly normalized, towards a non-degenerate limiting random variable,
may be parameterized as , ρ < 0, β∈ℝ, where β and ρ are second order parameters. The estimation of ρ, the “shape” second order parameter has been extensively addressed in the literature, but practically nothing has been done
related to the estimation of the “scale” second order parameter β. In this paper, and motivated by the importance of a reliable β-estimation in recent reduced bias tail index estimators, we shall deal with such a topic. Under a semi-parametric framework,
we introduce a class of β-estimators and study their consistency. We deal with the conditions enabling us to get the asymptotic normality of the members
of this class, and we illustrate the behaviour of the estimators, through Monte Carlo simulation techniques.
Research partially supported by FCT / POCTI and POCI / FEDER. 相似文献
17.
The Douglas–Rachford algorithm is a popular method for finding zeros of sums of monotone operators. By its definition, the Douglas–Rachford operator is not symmetric with respect to the order of the two operators. In this paper we provide a systematic study of the two possible Douglas–Rachford operators. We show that the reflectors of the underlying operators act as bijections between the fixed points sets of the two Douglas–Rachford operators. Some elegant formulae arise under additional assumptions. Various examples illustrate our results. 相似文献
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19.
20.
We investigate the so-called critical 2nth-order Sturm–Liouville difference operators and associated symmetric banded matrices. We show that arbitrarily small (in a certain sense) negative perturbation of a non-negative critical operator leads to an operator which is no longer non-negative. 相似文献