某些可微函数类的N宽度

N width of some differentiable function classes

文中借助Jensen不等式,样条函数等工具研究了Orlicz空间中定义域为[-π,π]的非周期函数类W^(r)L_(M)*在L_(1)内Kolmogorov宽度的渐近精确估计及其渐近最优子空间.并进一步对于该函数类的对偶形式,在L_(1)空间的对偶空间L_(∞)空间内讨论了其Kolmogorov宽度,线性宽度的渐近精确估计,特别地,给出Gelfand宽度对偶形式的精确估计.

In this paper,with the help of Jensen’s inequality,spline function and other tools,the Kolmogorov width of the aperiodic function class W^(r)L_(M)* whose domain is[-π,π]in Orlicz space is studied in L_(1) Asymptotically exact estimation and its asymptotically optimal subspace.Further,for the dual form of this function class,in the dual space L_(∞) space of L_(1) space,its Kolmogorov width,the asymptotic of linear width are discussed Near-exact estimates,in particular,give exact estimates of the Gelfand width dual form.