17 citations · 18 across the 12 of their papers we have counts for
5 papers · 2 filters
2-Normed D-Modules and Hahn-Banach Theorem for D-linear 2-functionals
Kulbir Singh, Romesh Kumar
In this paper we introduce the notion of D-valued 2-norm on hy- perbolic or D-valued modules. Further, we define D-linear 2-functional on these modules and consider some of their p…
Some Fundamental Theorems of Functional Analysis with Bicomplex and Hyperbolic Scalars
Heera Saini Aditi Sharma, Romesh Kumar
We discuss some properties of linear functionals on topological hyperbolic and topological bicomplex modules. The hyperbolic and bicomplex analogues of the uniform boundedness prin…
Topological Bicomplex Modules
Romesh Kumar, Heera Saini
In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski func…
Maximal Ideals in a Bicomplex Algebra and Bicomplex Gelfand-Mazur Theorem
Kulbir Singh, Romesh Kumar
In this paper we study the maximal ideals in a commutative ring of bicomplex numbers and then we describe the maximal ideals in a bicomplex algebra. We found that the kernel of a n…
Bicomplex Weighted Hardy Spaces and Bicomplex C*-algebras
Romesh Kumar, Kulbir Singh, Heera Saini +1
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 generaliz…