单连通区域上解析函数的插值问题

本文利用单位圆盘上Hardy空间插值问题的已知结论,用较初等的方法,对边界至少含有两个不同点的任意单连通区域,给出插值问题有解的充分必要条件。     

One-sided N-widths of some classes of periodic functions

In this paper,we determine the exact estimation of one-sided n-widthsd_n~+(w_q~r(p_r),L_1).q=1,∝,where W_q~r(P_r)is a class of differentiable 2π-periodic functions,and is determined by a differential opera-tor P_r(D)=D~σ∏_(j=t)~l(D-α_j),σ,j∈N,σ≥2,x_j≠0,x_j∈R.     

On certain classes of analytic functions

In this paper we introduce some new classes of analytic functions which generalise several known sequence spaces and function spaces studied by Simons, Maddox, Srivastava and others. We establish some inclusion relations, topological results and give the characterisation of continuous linear functionals for these spaces. Our results include the corresponding results of Simons, Maddox and others.     

N-widths for some classes of periodic functions with boundary conditions

For some classes of periodic functions with boundary conditions the strong asymptotics of the Kolmogorov's, the Gelfand's, and linear N-widths are obtained. The project supported by Doctoral Program Foundation of Institution of Higher Education and YNSFC.     

Norm estimates for convolution transforms of certain classes of analytic functions

For normalized analytic functions f in the unit disk Δ, we consider the class

     

On asymptotically exact estimates for the approximation of certain classes of functions by algebraic polynomials

We present a survey of results obtained for the last decade in the field of approximation of specific functions and classes of functions by algebraic polynomials in the spaces C and L ₁ and approximation with regard for the location of a point on an interval.     

How geodesics approach the boundary in a simply connected domain

This work was supported by NSF Grant DMS 92-04092 and an Alfred P. Sloan Research Fellowship.     

On the gap between two classes of analytic functions

Two large classes of analytic functions are defined, so that one contains the other. Sharp coefficient bounds for quadratic polynomials falling in the gap between these two classes are given.     

On classes of analytic functions related to conic domains

We introduce classes of analytic functions related to conic domains, using a new linear multiplier fractional differential operator (n∈N₀={0,1,…}, 0?α<1, λ?0), which is defined as

D⁰f(z)=f(z),     

On the approximate conformal mapping of the unit disk on a simply connected domain

We present a method of constructing the analytic function realizing an approximate conformal mapping of the unit disk on an arbitrary simply connected domain with the given smooth parametrically defined boundary. The method is based on a new boundary parameterization. Solution of the problem is reduced to the Fredholm integral equation of the second kind. We present the examples of three ways to solve the integral equation.