The purpose of this book is to develop the foundations of the theory of holomorphicity on the
ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with …

In this paper, we study the four-dimensional real algebra of bihyperbolic numbers. Under
consideration of the spectral representation of the bihyperbolic numbers, we give a partial …

In this paper, we develop topological modules over the ring of bicomplex numbers. We
discuss bicomplex convexity, hyperbolic-valued seminorms and hyperbolic-valued …

We consider modules over the commutative rings of hyperbolic and bicomplex numbers. In
both cases they are endowed with norms which take values in non–negative hyperbolic …

In this paper we study the bicomplex version of weighted Hardy spaces. Further, we
describe reproducing kernels for the bicomplex weighted Hardy spaces. In particular, we …

In this paper we introduce and study a functional calculus for bicomplex linear bounded
operators. The study is based on the decomposition of bicomplex numbers and of linear …

In this paper we study some basic properties of bicomplex linear operators on bicomplex
Hilbert spaces. Further, we introduce the notion of bicomplex quotient modules and …

We consider the notion of the Laurent series for the theory of bicomplex holomorphic
functions. Some basic properties of it are established. A special attention is paid to a …

In the theory of bicomplex holomorphic functions, there is not concept of isolated
singularities; that is, such functions do not have singularities just at a point like holomorphic …

We introduce the notion of a probabilistic measure which takes values in hyperbolic
numbers and which satisfies the system of axioms generalizing directly Kolmogorov's …