Canonical sine and cosine Transforms For Integrable Boehmians

TL;DR

This paper introduces canonical sine and cosine transforms, explores their properties, and extends these transforms to the space of integrable Boehmians, establishing foundational convolution theorems.

Contribution

It defines and analyzes canonical sine and cosine transforms, extends them to integrable Boehmians, and proves related convolution theorems in this new context.

Findings

Established convolution theorems for the transforms.

Extended transforms to the space of integrable Boehmians.

Provided foundational properties of the transforms in new function spaces.

Abstract

In this paper we define canonical sine and cosine transform, convolution operations, prove convolution theorems in space of integrable functions on real space. Further, obtain some results require to construct the spaces of integrable Boehmians then extend this canonical sine and canonical cosine transforms to space of integrable Boehmians and obtain their properties.