共查询到20条相似文献,搜索用时 93 毫秒
1.
Given α ∈ [0, 1], let h α (z):= z/(1 - αz), z ∈ D:= {z ∈ D: |z| < 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to h α if there exists δ ∈ (-π/2, π/2) such that Re{eiδ zf′(z)/h α (z)} > 0, z ∈ D. For the class ? (h α ) of all close-to-convex functions with respect to h α , the Fekete-Szegö problem is studied. 相似文献
2.
Rodrigo Ponce 《Israel Journal of Mathematics》2017,219(2):727-755
We characterize completely the well-posedness on the vector-valued Hölder and Lebesgue spaces of the degenerate fractional differential equation D α (Mu)(t) = Au(t) + f(t), t ∈ ? by using vector-valued multiplier results in the spaces C γ (?;X) and L p (?;X), where A and M are closed linear operators defined on the Banach space X, 0 < γ < 1, 1 < p < ∞, the fractional derivative is understood in the sense of Caputo and α is positive. 相似文献
3.
Konstantin Khanin Saša Kocić 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):200-207
For any α ∈ (0, 1), c ∈ ?+ \ {1} and γ > 0 and for Lebesgue almost all irrational ρ ∈ (0, 1), any two C 2+α -smooth circle diffeomorphisms with a break, with the same rotation number ρ and the same size of the breaks c, are conjugate to each other via a C 1-smooth conjugacy whose derivative is uniformly continuous with modulus of continuity ω(x) = A|log x|?γ for some A > 0. 相似文献
4.
The aim of this paper is to pursue the investigation of the phase retrieval problem for the fractional Fourier transform F α started by the second author. We here extend a method of A. E. J. M. Janssen to show that there is a countable set Q such that for every finite subset A ? Q, there exist two functions f, g not multiple of one another such that |F α f| = |F α g| for every α ∈ A.This is done by constructing two functions ?, ψ such that F α ? and F α ψ have disjoint support for each α ∈ A. To do so, we establish a link between F α [f], α ∈ Q and the Zak transform Z[f] generalizing the well known marginal properties of Z. 相似文献
5.
We investigate the equiconvergence on TN = [?π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N ? 1 components which are elements of “lacunary sequences.” 相似文献
6.
We consider a fractional Adams method for solving the nonlinear fractional differential equation \(\,^{C}_{0}D^{\alpha }_{t} y(t) = f(t, y(t)), \, \alpha >0\), equipped with the initial conditions \(y^{(k)} (0) = y_{0}^{(k)}, k=0, 1, \dots , \lceil \alpha \rceil -1\). Here, α may be an arbitrary positive number and ?α? denotes the smallest integer no less than α and the differential operator is the Caputo derivative. Under the assumption \(\,^{C}_{0}D^{\alpha }_{t} y \in C^{2}[0, T]\), Diethelm et al. (Numer. Algor. 36, 31–52, 2004) introduced a fractional Adams method with the uniform meshes t n = T(n/N),n = 0,1,2,…,N and proved that this method has the optimal convergence order uniformly in t n , that is O(N ?2) if α > 1 and O(N ?1?α ) if α ≤ 1. They also showed that if \(\,^{C}_{0}D^{\alpha }_{t} y(t) \notin C^{2}[0, T]\), the optimal convergence order of this method cannot be obtained with the uniform meshes. However, it is well-known that for y ∈ C m [0,T] for some \(m \in \mathbb {N}\) and 0 < α < m, the Caputo fractional derivative \(\,^{C}_{0}D^{\alpha }_{t} y(t) \) takes the form “\(\,^{C}_{0}D^{\alpha }_{t} y(t) = c t^{\lceil \alpha \rceil -\alpha } + \text {smoother terms}\)” (Diethelm et al. Numer. Algor. 36, 31–52, 2004), which implies that \(\,^{C}_{0}D^{\alpha }_{t} y \) behaves as t ?α??α which is not in C 2[0,T]. By using the graded meshes t n = T(n/N) r ,n = 0,1,2,…,N with some suitable r > 1, we show that the optimal convergence order of this method can be recovered uniformly in t n even if \(\,^{C}_{0}D^{\alpha }_{t} y\) behaves as t σ ,0 < σ < 1. Numerical examples are given to show that the numerical results are consistent with the theoretical results. 相似文献
7.
Leilei Wei 《Numerical Algorithms》2018,77(3):675-690
In this paper, we first present a new finite difference scheme to approximate the time fractional derivatives, which is defined in the sense of Caputo, and give a semidiscrete scheme in time with the truncation error O((Δt)3?α ), where Δt is the time step size. Then a fully discrete scheme based on the semidiscrete scheme for the fractional Cattaneo equation in which the space direction is approximated by a local discontinuous Galerkin method is presented and analyzed. We prove that the method is unconditionally stable and convergent with order O(h k+1 + (Δt)3?α ), where k is the degree of piecewise polynomial. Numerical examples are also given to confirm the theoretical analysis. 相似文献
8.
V. F. Babenko N. V. Parfinovich 《Proceedings of the Steklov Institute of Mathematics》2012,277(1):9-20
Let L ∞,s 1 (? m ) be the space of functions f ∈ L ∞(? m ) such that ?f/?x i ∈ L s (? m) for each i = 1, ...,m . New sharp Kolmogorov type inequalities are obtained for the norms of the Riesz derivatives ∥D α f∥∞ of functions f ∈ L ∞,s 1 (? m ). Stechkin’s problem on approximation of unbounded operators D α by bounded operators on the class of functions f ∈ L ∞,s 1 (? m ) such that ∥?f∥ s ≤ 1 and the problem of optimal recovery of the operator D α on elements from this class given with error δ are solved. 相似文献
9.
Let G be a graph, and g, f: V (G) → Z+ with g(x) ≤ f(x) for each x ∈ V (G). We say that G admits all fractional (g, f)-factors if G contains an fractional r-factor for every r: V (G) → Z+ with g(x) ≤ r(x) ≤ f(x) for any x ∈ V (G). Let H be a subgraph of G. We say that G has all fractional (g, f)-factors excluding H if for every r: V (G) → Z+ with g(x) ≤ r(x) ≤ f(x) for all x ∈ V (G), G has a fractional r-factor F h such that E(H) ∩ E(F h ) = θ, where h: E(G) → [0, 1] is a function. In this paper, we show a characterization for the existence of all fractional (g, f)-factors excluding H and obtain two sufficient conditions for a graph to have all fractional (g, f)-factors excluding H. 相似文献
10.
A. M. Sedletskii 《Doklady Mathematics》2016,94(1):464-467
Let B be one of the spaces Lp(?π,π), 1 ≤ p < ∞, p ≠ 2, and C[?π,π]. Sufficient conditions under which the “perturbed” trigonometric system \({e^{i{{\left( {n + {\alpha _n}} \right)}^t}}}\), n ∈ Z, is equivalent in B to the trigonometric system eint, n ∈ Z, are found. Under an additional requirement on (αn), a necessary condition is obtained. One of the results is as follows. If (αn) ∈ ls, where 1/s = 1/p - 1/2, then the equivalence specified above takes place, and the exponent s is exact; the space C corresponds to p = ∞. The proofs are based on the application of Fourier multipliers. 相似文献
11.
In this paper, we obtain a version of the John–Nirenberg inequality suitable for Campanato spaces Cp,β with 0 < p < 1 and show that the spaces Cp,β are independent of the scale p ∈ (0,∞) in sense of norm when 0 < β < 1. As an application, we characterize these spaces by the boundedness of the commutators [b,B α ] j (j = 1, 2) generated by bilinear fractional integral operators B α and the symbol b acting from Lp1 × Lp2 to L q for p1, p2 ∈ (1,∞), q ∈ (0,∞) and 1/q = 1/p1 + 1/p2 ? (α + β)/n. 相似文献
12.
Let G be a finite p-group. The automorphism α of a group G is said to be an absolute central automorphism, if for all x ∈ G, x -1 x α ∈ L(G), where L(G) is the absolute center of G.In this paper, we obtain a necessary and sufficient condition that each absolute central automorphism of G fixes the center element-wise. 相似文献
13.
In this paper we study obstacle problems for the Navier (spectral) fractional Laplacian (?ΔΩ) s of order s ∈ (0,1) in a bounded domain Ω ? R n . 相似文献
14.
The authors study a porous medium equation with a right-hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator.The derivative in time is also fractional and is of Caputo-type, which takes into account"memory". The precise model isD_t~αu- div(u(-Δ)~(-σ)u) = f, 0 σ 1/2.This paper poses the problem over {t ∈ R~+, x ∈ R~n} with nonnegative initial data u(0, x) ≥0 as well as the right-hand side f ≥ 0. The existence for weak solutions when f, u(0, x)have exponential decay at infinity is proved. The main result is H¨older continuity for such weak solutions. 相似文献
15.
16.
Zong Xiju Zhao Yi Yin Zhaoyang Chi Tao 《高校应用数学学报(英文版)》2007,22(3):277-285
In this paper, the boundary control problem of a distributed parameter system described by the Schr(o)dinger equation posed on finite interval α≤ x ≤β:{iyt yxx |y|2y = 0,y(α,t) = h1(t),y(β,t) = h2(t) for t > 0 (S)is considered. It is shown that by choosing appropriate control inputs (hj), (j = 1,2) one can always guide the system (S) from a given initial state ψ∈ Hs(α,β),(s ∈ R) to a terminal state ψ∈ Hs(α,β), in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of Schr(o)dinger equation posed on the whole line R. The discovered smoothing properties of Schr(o)dinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of (semi-linear) nonlinear Schr(o)dinger equation. 相似文献
17.
Michael I. Ganzburg 《Journal d'Analyse Mathématique》2018,135(2):389-411
Let μ be a measurewith a k-concave density W on an open convex set V in Rm, that is, W is an integrable weight satisfying the condition for all x ∈ V, y ∈ V, and α ∈ [0, 1]. In this paper, we first show that the Fradelizi μ-distributional inequalities for polynomials P of m variables are sharp for each m and k ∈ (?1/m,∞]. Classes of extremal sets V, weights W, and polynomials P for these inequalities are presented. Sharpness of the Bobkov-Nazarov-Fradelizi dilation-type inequalities is established as well. Second, we find efficient conditions for k-concavity of a weight W and obtain new sharp polynomial inequalities.
相似文献
$$W(ax + (1 - a)y) \geqslant {(a{W^K}(x) + (1 - a){W^K}(y))^{1/k}},k \in ( - 1/m,\infty ]$$
18.
The spaces χ p,α induce a classification of the closed subsets Θ ofT, the reals modulo 1, as sets of (p,α) multiplicity (or (p, α uniqueness) as Θ is (or is not) the support of a non-zero distribdtion ψ such that ψ4 (n) ∈ χ p,α . 相似文献
19.
William A. Veech 《Journal d'Analyse Mathématique》2018,135(2):413-436
Let S be the set of square-free natural numbers. A Hilbert-Schmidt operator, A, associated to the Möbius function has the property that it maps from \({ \cup _{0 < r < \infty }}{l^r}(s)\) to \({ \cap _{0 < r < \infty }}{l^r}(s)\), injectively. If 0 < r< 2 and ξ ∈ lr (S), the series \({f_\zeta } = \sum\nolimits_{n \in s} {A\zeta (x)cos2\pi nx} \) converges uniformly to an element of fξR0, i.e., a periodic, even, continuous function with equally spaced Riemann sums, \(\sum\nolimits_{j = 0}^{N - 1} {{f_\zeta }} (j/N) = 0,N = 1,2....\) If \({A_{\zeta \lambda }} = \lambda {\zeta _\lambda },{\zeta _\lambda }(1) = 1\), then ξλ is multiplicative. If \({f_{{\zeta _\lambda }}} \in {\Lambda _a}\), the space of α-Lipschitz continous functions, for some α > 0, and if χ is any Dirichlet character, then L(s, χ) ≠ 0, Res > 1 ? α. Conjecturally, the Generalized Riemann Hypothesis (GRH) is equivalent to fξ ∈ Λα, α < 1/2, ξ ∈ lr (S), 0 < r < 2. Using a 1991 estimate by R. C. Baker and G. Harman, one finds GRH implies fξ ∈ Λα, α < 1/4, ξ ∈ lr (S), 0 < r < 2. The question of whether R0 ∩ Λα ≠ {0} for some positive α > 0 is open. 相似文献
20.
Let(Σ, g) be a compact Riemannian surface without boundary and λ_1(Σ) be the first eigenvalue of the Laplace-Beltrami operator ?_g. Let h be a positive smooth function on Σ. Define a functional J_(α,β)(u) =1/2∫Σ(|?_gu|~2-αu~2)dv_g-β log∫Σhe~udv_g on a function space H = {u ∈ W~(1,2)(Σ) :∫Σudvg = 0}. If α λ_1(Σ) and J_(α,8π) has no minimizer on H,then we calculate the infimum of Jα,8π on H by using the method of blow-up analysis. As a consequence,we give a sufficient condition under which a Kazdan-Warner equation has a solution. If αλ_1(Σ), then infu∈HJ_(α,8π)(u) =-∞. If β 8π, then for any α∈ R, there holds infu∈H Jα,β(u) =-∞. Moreover, we consider the same problem in the case that α is large, where higher order eigenvalues are involved. 相似文献