Relativistic formulation of abstract evolution equations

TL;DR

This paper introduces a relativistic framework for abstract evolution equations, demonstrating the existence of a logarithmic representation that applies without invertibility assumptions, enabling analysis of nonlinear and discrete properties.

Contribution

It presents a novel relativistic formulation and logarithmic representation for abstract evolution equations, extending analysis capabilities beyond traditional invertibility constraints.

Findings

Logarithmic representation exists without invertibility assumptions

Nonlinear properties are valid for infinitesimal generators

Discrete properties are applicable to relativistic evolution equations

Abstract

The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the logarithmic representation of operators, nonlinear and discrete properties are shown to be valid to the infinitesimal generators of relativistic abstract evolution equations.