函数空间的小波逼近

Wavelets Approximation in Functional Spaces

从研究Sobolev空间中函数的逼近入手,利用正交级数的分解来估计函数空间的模,用多分辨率分析构造逼近的性能,找到了Sobolev空间中基于小波逼近的函数的等价性描述和模的等价形式,并且类似地在Besov空间中进行讨论,给出了Besov空间中函数的等价性描述定理和模的等价形式以及相关证明过程,这一结论成为深入刻画函数空间的又一有效工具.

Starting with approximation of functions in Sobolev spaces,by using the decomposition of orthonormal series to estimate the modulus in a functional space and constructing the characters of the approximation by multi-resolution analysis,an equivalent description of wavelet approximation in Sobolev spaces and the equivalent form of the modulus are obtained.Similar discussion in Besov spaces gives the equivalent theorem of the functions and the form of the modulus in these spaces.The conclusions provide another efficient tool for us to describe functional space.