Analysis Mathematica最新文献

Given an expansive matrix R ∈ M_d(ℤ) and a finite set of digit B taken from ℤ^d/R(ℤ^d). It was shown previously that if we can find an L such that (R, B, L) forms a Hadamard triple, then the associated fractal self-affine measure generated by (R, B) admits an exponential orthonormal basis of certain frequency set Λ, and hence it is termed as a spectral measure. In this paper, we show that if #B < ∣det(R)∣, not only it is spectral, we can also construct arbitrarily sparse spectrum Λ in the sense that its Beurling dimension is zero.

In this paper, we continue some recent work on two weight boundedness of sparse operators to the “off-diagonal” setting. We use the new “entropy bumps” introduced in by Treil and Volberg and improved by Lacey and Spencer [11] and the “direct comparison bumps” introduced by Rahm and Spencer [23] and improved by Lerner [14]. Our results are “sharp” in the sense that they are sharp in various particular cases. A feature is that given the current machinery and advances, the proofs are almost trivial.

We obtain necessary conditions for certain type of rational delay-differential equations to allow the existence of a non-rational meromorphic solution with hyper-order less than one. In addition, we give a further discussion of the coefficients of a delay-differential equation with fixed degree.

The nth derivative criterion for functions belonging to the Dirichlet–Morrey space ({cal D}_p^lambda ) is given in this paper. Furthermore, two sufficient conditions for coefficients of the complex linear differential equation

are obtained such that all solutions belong to ({cal D}_p^lambda ), where A_j(z) are analytic functions in the unit disc, j = 0,…,n.

We study the following question: which monotonicity order implies upper and lower estimates of the sum of a sine series (gleft( {{boldsymbol{b}},x} right) = sumnolimits_{k = 1}^infty {{b_k}} ) sin kx near zero in terms of the function (vleft( {{boldsymbol{b}},x} right) = xsumnolimits_{k = 1}^{left[ {pi /x} right]} {k{b_k}} ). Our results complete, on a qualitative level, the studies began by R. Salem and continued by S. Izumi, S. A. Telyakovskiĭ and A. Yu. Popov.

We obtain a characterization of the weighted Besov space ({{cal B}_K}left( p right)) for a weight function K, 0 < p < ∞, in terms of symmetric and derivative-free double integrals with the weight function K in the unit disc. As a by-product, we give a modification of the identity of Littlewood—Paley type for the Bergman space. As an application, a derivative-free characterization of ({{cal Q}_K}) type spaces is obtained.

We study mappings defined in the domain of a metric space that distort the modulus of families of paths by the type of the inverse Poletsky inequality. It is proved that such mappings have a continuous extension to the boundary of the domain in terms of prime ends. Under some additional conditions, the families of such mappings are equicontinuous in the closure of the domain with respect to the space of prime ends.

We construct an absolutely convergent Dirichlet series connected to the classical Hurwitz zeta-function. The shifts of this function approximate analytic functions defined in the right-hand side of the critical strip.

The aim of this paper is to introduce the Dunkl—Hilbert transform H^k, with k ≥ 0, induced by the Dunkl differential operator and associated with the reflection group ℤ₂. For this end, we establish that the Dunkl—Poisson kernel and the conjugate Dunkl—Poisson kernel satisfy the Cauchy—Riemann equations in the Dunkl context. We prove the continuity of H^k on L^p(w_k) for 1 < p < ∞, where w_k(x) = ∣x∣^2k. Finally, we introduce the maximal Hilbert operator H ^k_* and establish an analogue of Cotlar’s theorem.

In this paper, we study some geometric properties in Banach lattices and the class of almost limited completely continuous operators. For example, we study Banach lattices with property (d) and we give a new characterization of this property in terms of the solid hull of almost limited sets.