A multiplier theorem using the Schechter's method of interpolation

Let m be a measurable bounded function and let us assume that there exists a bounded functions S so that m(ξ)S(ξ)^it−1 is a Fourier multiplier on L^p uniformly in . Then, using the analytic interpolation theorem of Stein, one can show that necessarily m is a L^p multiplier. The purpose of this work is to show that under the above conditions, it holds that, for every , m(log S)^kM_p. The technique is based on the Schechter's interpolation method.     

Inverse spectral problems for Sturm-Liouville operators with singular potentials. Part III: Reconstruction by three spectra

We solve the inverse spectral problem of recovering the singular potential from W⁻¹₂(0,1) of a Sturm-Liouville operator by its spectra on the three intervals [0,1], [0,a], and [a,1] for some a∈(0,1). Necessary and sufficient conditions on the spectral data are derived, and uniqueness of the solution is analyzed.     

Two families of functions related to the fractional powers of generators of strongly continuous contraction semigroups

Two families of functions on (0,∞) are related to the theory of fractional powers of generators of strongly continuous semigroups—namely the family (σ_α(·,t))_t>0 of density functions of the one-sided stable semigroup of order α∈(0,1), and a family (e_α(·,μ))_μ>0 of Mittag-Leffler type functions. For the latter family we make this relation visible. We collect some important properties of these functions, and we improve a known result on the Laplace transform of the functions e_α(·,μ) and their derivatives in the sense that we enlarge the domains of the Laplace variable. We furthermore find an expression for the Laplace transform of the functions t?σ_α(x,t), x>0, in terms of the derivative e′_α(·,μ).     

次线性算子在齐型空间的弱Herz-Morrey空间上的有界性

作者在齐型空间上定义了Herz-Morrey空间。并研究了某些次线性算子在弱HHerz-Morrey空间上的有界性．     

A Variational Problem for Steady Vortices in a Shear Flow Past an Obstacle

We prove existence of maximizers for a variational problem for a steady vortex anomaly of bounded extent in a shear flow, past an obstacle, in a planar exterior domain. Kinetic energy is maximized subject to the vorticity being a rearrangement of a prescribed function.     

ON CONVERGENCE RATE OF APPROXIMATION FOR TWO-DIMENSIONAL BASKAKOV OPERATORS

In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights making use of multivariate decompose skills and results of one-dimensional Baskakov operators, and obtain the direct approximationtheorem.     

A New Hierarchy Soliton Equations Associated with a Schrdinger Type Spectral Problem and the Corresponding Finite-dimensional Integrable System

By introducing a Schrodinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.     

实数轴上Gr nwald插值算子的收敛性

考虑了拓展插值结点取值范围后的Gr nwald插值算子在实数轴上的收敛性,证明了将结点范围扩大到全实轴后,即取为Hermite多项式的零点,对任意点x∈(-∞,∞),有Gn(f,x)→f(x),n→∞,其中,f(x)为实数轴上任一满足|f(x)|=O(ex2/2)的连续函数.