Functions and Analysis

2209 Submissions

[3] viXra:2209.0134 [pdf] submitted on 2022-09-24 09:58:07

New Principles of Dierential Equations VI

Authors: Hong Lai Zhu
Comments: 59 Pages.

This paper uses Z transformations to get the general solutions of many second-order, third-order and fourth-order linear PDEs for the first time, and uses the general solutions to obtain the exact solutions of many typical definite solution problems. We present the Z4 transformation for the first time and use it to solve a specific case. We successfully get the Fourier series solution by the series general solution of the one-dimensional homogeneous wave equation, which successfully solves a famed unresolved debate in the history of mathematics.
Category: Functions and Analysis

[2] viXra:2209.0080 [pdf] submitted on 2022-09-14 00:43:36

The Second Order Shannon Total Generalized Variation for Image Restoration

Authors: Alireza Hosseini, Sohrab Bazm
Comments: 26 Pages.

The Second Order Shannon Total Generalized Variation for Image Restoration.
Category: Functions and Analysis

[1] viXra:2209.0077 [pdf] submitted on 2022-09-13 01:01:53

Norm Inequalities for One Dimensional Sobolev Hilbert Spaces (An Extension)

Authors: Saburou Saitoh
Comments: 12 Pages.

In this paper, we shall consider norm inequalities for one dimensional Sobolev Hilbert spaces by using the theory of reproducing kernels as fundamental inequalities.
Category: Functions and Analysis