Applications of the theory of reproducing kernels to the Tikhonov regularization

我们得到了离散微分方程组的概念，并得到了各种具体结果。对于有限数量的输入数据，我们得到了一个新的概念，即我们可以给出自然输入数据作为其他输入数据。介绍了一般分式函数的新定义及其表示，以及如何用计算机进行实际计算的方法。给出了卷积型核、Toeplitz核和Hankel核的积分方程解的近似解。给出了新的卷积和相关的卷积范数不等式。我们写了一本314页的新研究书稿。

We obtained the concept of discrete differential equations and derived various concrete results. For a finite number of input data, we obtain a new concept that we can give natural input data as other input data. We introduced the new definition of general fractional functions and their representations, and methods how to calculate them practically, by computers. We gave the approximate solutions of integral equations with convolution type kernels and with Toeplitz and Hankel kernels. New convolutions and related convolution norm inequalities were derived. We wrote a new research book manuscript with 314 pages.