Discrete Calculus By Analogy

Discrete Calculus By Analogy

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Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral ...
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Appendix A 2-Variable Discrete Analysis

Pp. 101-140 (40)

F. A. Izadi

Abstract

This chapter deals with ten different problems. Except for the three sections; namely an unsolved problem about a cubic root of a complex number, symmetric derivative, and the spectral de- composition of a matrix by a projection matrices, all other sections are devoted to the discrete analysis of complex valued functions. Topics included are the discrete partial derivatives of complex valued functions, the Cauchy theorem, Laplace equation, Cauchy-Riemann discrete differential equations, complex integra- tion and above all, the most important concept which brings all these together, is the discrete analog of analytic functions in complex analysis.

Affiliation:

Toronto Canada