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In this paper, we investigate a class of modified G-transforms having G-functions as kernels on a generalized space of sequences. We derive certain spaces of generalized functions named as Boehmians to legitimate the existence of the described integral. The modified G-transform is partially sharing the classical transform with some general properties. An inversion formula is also discussed on the generalized sense. [ABSTRACT FROM AUTHOR]

In this paper we establish certain spaces of Boehmians for the generalized Hankel integral transform lη;σ,w;κ,λ. We estimate the generalization lgeη;σ;w;κ;λ of lη;σ,w;κ,λ and explore some of its properties. Continuity of lgeη;σ;w;κ;λ with respect to δ and Δ - convergence is also discussed in some detail. [ABSTRACT FROM AUTHOR]

Integral transforms of strong Boehmians have not yet been reported in the literature. Perhaps, because the strong Boehmian space is not widely known nor used [10]. In this article, we derive certain space of Boehmians (the space of stronge Boehmians) which handle the Fourier transform with a different performance. The Fourier transform of a strong Boehmian has been established as a one-to-one mapping which is continuous with respect to δ and Δ convergence. The inverse Fourier transform is also defined and some of its properties are obtained. Related theorems are discussed in some detail. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Struve transformation on certain space of Boehmians. The transform under consideration is defined and some of its properties are also illustrated . [ABSTRACT FROM AUTHOR]

Integral transforms have been introduced and found their application in certain boundary value problems. The Natural transform is closely connected to the Laplace and Sumudu transforms. In the present paper, we discuss the Natural transform on certain spaces of generalized functions. We obtain the Natural transform for a space of distributions and further investigate the cited transform on space of Boehmians. More results are also established. [ABSTRACT FROM AUTHOR]

We extend the Fresnel-wavelet transform to the context of generalized functions, namely, Boehmians. At first, we study the Fresnel-wavelet transform in the sense of distributions of compact support. Based on this concept, we introduce two new spaces of Boehmians and proving certain related results. Further, we show that the extended transform establishes a linear and an isomorphic mapping between the Boehmian spaces. Moreover, conditions of continuity of the extended transform and its inverse with respect to δ and Δ convergence are discussed in some details. [ABSTRACT FROM AUTHOR]

Having defined spaces of ultradifferentiable functions along with an assigned spaces of tempered ultradistributions, certain spaces of multipliers are investigated and various continuous mappings are obtained. [ABSTRACT FROM AUTHOR]

This paper deals with ultradistributions for the Fourier sine (cosine) transform on a certain dual testing function space and tempered Boehmian and ultraBoehmian spaces. [ABSTRACT FROM AUTHOR]

Certain distributional and tempered distributional Fourier sine (cosine) transformations are discussed on certain testing function spaces. [ABSTRACT FROM AUTHOR]