Kadison-Singer transform (KS-transform) is introduced as a multiplicative Fourier transform associated with the multiplicative structure of natural numbers. It is a unitary operator between the Hilbert space L2([1,∞)) and Hardy space H2(Ω), where Ω is a the right half complex plane with the real part great than or equal to 1/2. We also show that KS-transform maps the multiplicative convolution of two functions on[1,∞) to the usual product of functions on Ω. Riemann hypothesis is equivalent to the vanishing index of certain convolution operators.
This paper considers pointwise deconvolution estimation of density functions under the local Hölder condition by wavelet method. We firstly give a lower bound of any estimator with super-smooth noises. Then the practical linear wavelet estimator is constructed to obtain the optimal convergence rate, which means that the rate coincides with the lower bound. The strong convergence rate of the defined wavelet estimator is also provided. It should be pointed out that all above estimations are adaptive.
Let AT (Δ) be the asymptotic Teichmüller space on the unit disk Δ, viewed as the space of all asymptotic Teichmüller equivalence classes[[μ]] or[[f μ]]. It is shown that, for each asymptotically extremal[[f μ]] in AT (Δ), there exists an asymptotically extremal gν in[[f μ]] such that the boundary dilatation h*(μf?g-1(g(z))) =0. A parallel result in the tangent space to AT (Δ) at the basepoint is also obtained.
In this paper, we investigate a uniqueness of meromorphic functions with finite order concerning their derivative and difference and obtain one result that if f' and Δcf share a, b,∞ CM, then f' ≡ Δcf. This result confirms the problem of Qi et al. in 2018.
In[Anomaly cancellation and modularity, Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics, 2014:87-104, World Sci. Publ., Hackensack, NJ], Han-Liu-Zhang gave a anomaly cancellation formula which generalized the Green-Schwarz formula and the Schwartz-Witten formula. In this paper, we give two generalized Han-Liu-Zhang formulas and a Han-Liu-Zhang formula in odd dimension is also given. By studying modular invariance properties of some characteristic forms, some new anomaly cancellation formulas in odd dimension are given.
Consider the near-critical random walk on a strip. By the explicit criteria for recurrence and transience, with the help of asymptotic theory of the solution of linear difference system with disturbance, and the propositions of matrix norm, we give a recurrence classification in terms of the order of the perturbation matrix.
In terms of Bressan and Constantin's arguments in 2007, by exploiting the balance law and some estimates, we prove the existence of global dissipative solutions for the Dullin-Gottwald-Holm equation with a forcing term in H1(R).
The aim of this paper is to introduce a new viscosity iterative algorithm for finding a common element of the set of solutions of a new variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of a nonexpansive mapping in Hilbert spaces. We give several strong convergence theorems under some suitable assumptions imposed on the parameters by using modified extragradient method. A numerical example is also given to support our main results. The results obtained in this paper extend and improve many recent ones.
We generalize the Liggett-Stroock inequality of the time homogeneous Markov process to the inhomogeneous Markov process, and establish the relationship between the transition semigroup of inhomogeneous Markov process and the Liggett-Stroock inequality.
In this paper, concerning some truncated counting functions with different weights, we prove a new second main theorem for meromorphic mappings from Cn into PN (C). By using the new second main theorem, we consider the uniqueness problem for the case of degenerate meromorphic mappings sharing moving hyperplanes located in general position, and a uniqueness result is obtained under some weak conditions, which can be seen as an improvement of previous well-known results.
In this paper, the authors investigate some properties of the normal weight Zygmund space Zμ(B) in several complex variables. Firstly, the authors establish an integral representation of function in Zμ(B). Secondly, the authors show that Zμ(B) can be identified with the dual space of the normal weight Bergman space Aν1 (B) under the integral pairing
where ν(r)=(1-r2)β+1μ-1(r) (0 ≤ r<1) and β>max{0, b-1}. Finally, as an application of the integral representation and the dual, the authors give an atomic decomposition for every function in Zμ(B).
The generalized Jordan-von Neumann type constant is introduced, some basic properties of this new constant are investigated. Moreover, The weakly convergent sequence coefficient WCS(X) is estimated by the generalized Jordan-von and Neumann type constant, the weak orthogonality coefficient μ(X) and Domínguez-Benavides coefficient R(1, X), which enables us to obtain some sufficient conditions for normal structure. The results obtained in this paper significantly improve some known results in the literatures.