An estimate of Sumudu transforms for Boehmians

On Diffraction Fresnel Transforms for Boehmians

and Applied Analysis 3 Proof. Let ξ be fixed. If φ t is in S, then its diffraction Fresnel transform certainly exists. Moreover, differentiating the right-hand side of 2.3 with respect to ξ, under the integral sign, ktimes, yields a sum of polynomials, pk t ξ , say of combinations of t and ξ. That is, ∣ ∣ ∣ ∣ ∣ d dtk Fd ( φ ) ξ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ pk t ξ φ t exp ( i ( α1t 2 − 2tξ α2ξ ) 2γ1 )∣ ∣...

A note on the comparison between Laplace and Sumudu transforms

Boehmians of type S and their Fourier transforms

Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.

Integrable Boehmians, Fourier Transforms, and Poisson’s Summation Formula

Boehmians are classes of generalized functions whose construction is algebraic. The first construction appeared in a paper that was published in 1981 [6]. In [8], P. Mikusiński constructs a space of Boehmians, βL1(R), in which each element has a Fourier transform. Mikusiński shows that the Fourier transform of a Boehmian satisfies some basic properties, and he also proves an inversion theorem. ...

q-Sumudu Transforms of q-Analogues of Bessel Functions

The main purpose of this paper is to evaluate q-Sumudu transforms of a product of q-Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of q-Sumudu transforms to the solutions of the q-integrodifferential equations involving q-Bessel functions. The results may help to extend the q-theory of orthogona...