Clifford analysis is a higher-dimensional function theory offering a generalization of the theory of holomorphic functions in the complex plane and, at the same time, a refinement of classical harmonic analysis.
Pullback attractor theory is a natural generalization of the theory of global attractors developed to study autonomous dynamical systems, and it is well suited to study the non-autonomous dynamical systems.
Clifford analysis essentially is a higher dimensional function theory offering both a generalization of the theory of holomorphic functions in the complex plane and a refinement of classical multidimensional harmonic analysis.
This modification or extension of the theory contributes to the analytical generalization of the theory.
In this view, type theory appears as a vast generalization of set theory, since a set is a particular kind of type.
Indeed, for Husserl, the theory of intentionality is a generalization of the theory of linguistic reference: as linguistic reference is mediated by sense, so intentional reference is mediated by noematic sense.
The study of multilinear averaging operators is traced back to the multilinear singular integral operator theory [16], and motivated not only the generalization of the theory of linear ones but also their natural appearance in analysis.
The theory of variational inequalities represents, in fact, a very natural generalization of the theory of boundary value problems and allows us to consider new problems arising from many fields of applied mathematics, such as mechanics, physics, engineering, the theory of convex programming, and the theory of control.
The method of exhaustion, also due to Eudoxus, was a generalization of the theory of proportions.
The multichannel generalization of the theory of spectral, scattering, and decay control is presented.
The electrophilic influence (through polarization) should also be included as a natural generalization of Millers' theory.
