Related papers: Integration of Bicomplex Valued Function along Hyp…
We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…
We define and solve boundary value problems of Schwarz and Dirichlet type on the complex unit disk for bicomplex-valued functions.
In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…
We explore the Bohr inequality involving the Fourier transforms of complex valued integrable and square integrable functions defined on a second countable compact topological group. We also investigate the connection of the Bohr phenomenon…
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in…
Assuming complex functions defined on complex curves satisfy recursion relations with respect to number of parameters, we express the corresponding cohomology theory via generalizations of holomorphic connections. In examples provided, the…
We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.
In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.
We undertake to develop a successful framework for commutative-associative hypercomplex numbers with the view to explicate and study associated geometric and generalized-relativistic concepts, basing on an interesting possibility to…
This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding…
In this article we describe the novel method to construct fundamental solutions for operators with variable coefficients. That method was introduced in "A note on the fundamental solution for the Tricomi-type equation in the hyperbolic…
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 properties. We also establish the Hahn- Banach type extension…
This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter's theory of regular, quaternionic functions. The algebras of quaternions…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…