Besov空间的小波刻划

Besov spaces contain many fundamental spaces, such as Sobolev spaces, Holder spaces, Zygmund class, Lipschitz spaces and etc. They can describe smoothness of functions and can be the solution spaces of certain partial differential equations. Operator characterizations for Besov spaces interest many mathematicians, because they are complicated and not easily understood. Wavelet characterization for those spaces are important. It is a meaningful course to match acceptable wavelets with Bescov spaces of arbitrary smoothness. In fact, when using a wavelet to detect the singularity of an underlying function from a given set of data, one normally does not know the smoothness of the underlying function. Hence, it is difficult to select a proper wavelet system that can characterize its smoothness. It is very much helpful to have one fixed nonstationary compactly supported wavelet frame that can characterize all Besov spaces.

Besov空间包含许多常见的函数空间, 如Sobolev空间, Holder空间, Zygmund类以及Lipschitz空间等. 它的重要性在于描述函数的光滑性以及被用做一些偏微分方程的解空间; 由于Besov空间的复杂性, 也为了更好地理解它, Besov空间的算子刻划受到了许多数学家的重视. 随着小波分析的出现, 小波基刻划Besov空间成为重要课题. 对于具有任意阶光滑性的Besov空间要匹配合适的小波刻划是有意义的, 事实上, 当把小波用于检测来自于某一数据集下的隐含的函数的奇异性时, 我们往往不知道其光滑性. 因此, 选择合适的能刻划光滑性的小波系统就变得困难起来, 所以一组能刻划所有Besov空间的非稳定紧支撑小波标架将是非常有帮助的.

Besov空间包含许多常见的函数空间, 如Sobolev空间, Holder空间, Zygmund类以及Lipschitz空间等. 它的重要性在于描述函数的光滑性以及被用做一些偏微分方程的解空间; 由于Besov空间的复杂性, 也为了更好地理解它, Besov空间的算子刻划受到了许多数学家的重视. 随着小波分析的出现, 小波基刻划Besov空间成为重要课题. 对于具有任意阶光滑性的Besov空间要匹配合适的小波刻划是有意义的, 事实上, 当把小波用于检测来自于某一数据集下的隐含的函数的奇异性时, 我们往往不知道其光滑性. 因此, 选择合适的能刻划光滑性的小波系统就变得困难起来, 所以一组能刻划所有Besov空间的非稳定紧支撑小波标架将是非常有帮助的.