Discrete Wiener algebra in the bicomplex setting, spectral factorization with symmetry, and superoscillations

Abstract

In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can be seen as a complex valued case and, in this matrix valued case, we make the necessary connection between bicomplex analysis and complex analysis with symmetry. We also write an application to superoscillations in this case.

A note on the complex and bicomplex valued neural networks

“…We recall the definition of bicomplex analyticity, a more recent concept in hypercomplex analysis, more details in [8,9,10,22,23].…”

“…Among these, for example, the authors have extended the complex perceptron algorithm to the bicomplex case in [5,6]. Inroads in bicomplex function theory and spaces have also been made by many, such as [8,9,10,22,23], to cite just a few. In 1960 Widrow and Hoff( [33]) have extended the gradient descent technique to the complex domain which was derived with respect to the real and imaginary part.…”