Related papers: Inverse Fourier Transform for Bi-Complex Variables
In this paper we examine the existence of bicomplexied inverse Laplacetransform as an extension of its complexied inverse version within theregion of convergence of bicomplex Laplace transform. In this course weuse the idempotent…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of…
We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional…
We consider and discuss some basic properties of the bicomplex analog of the classical Bargmann space. The explicit expression of the integral operator connecting the complex and bicomplex Bargmann spaces is also given. The corresponding…
A Fourier transform from momentum space to twistor space is introduced in twistor string theory, for the first time, for the case where the twistor space is a three-dimensional real projective space, corresponding to ultra-hyperbolic…
In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
In this article we have studied bicomplex valued measurable functions on an arbitrary measurable space. We have established the bicomplex version of Lebesgue's dominated convergence theorem and some other results related to this theorem.…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
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…
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…
We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after…