Published Paper Details:

This paper introduces and studies the Sumudu transform with parameter p, the Fourier transform with parameter s, and their combined structure, the Sumudu-Fourier transform (SFT). A generalized formulation of the SFT is developed in the framework of distributions of compact support, enabling its extension to a broad class of generalized functions in the dual space . The analyticity properties of both the classical and distributional SFT are investigated. By applying Cauchy's integral formula and exploiting appropriate growth conditions on corresponding kernels, we demonstrate that the Sumudu-Fourier transform is analytic in complex domains of the parameters p and s. The analyticity proofs rely on convergence of incremental ratios in the dual space and on uniform bounds for transform kernels. These results establish a rigorous mathematical foundation for parameter-dependent Sumudu-Fourier transforms and extend their applicability to generalized function spaces.