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September 23, 2025Far East Journal of Mathematical Sciences (FJMS)0 citationsOpen Access

Convolution Operator With a Weight Function for Hartley Integral Transform and Its Applications

Key Points

This convolution operator introduces a weight function, effectively enhancing the Hartley integral transform.
The operator is applied to solve a class of integral equations, particularly those of Toeplitz and Hankel types.
Necessary conditions for unitary operators in this context are established alongside the formulation of the Plancherel type theorem.
Results indicate that a sequence of functions can converge to the original function while highlighting the boundedness of these operators.

Abstract

In this paper, we introduce a new convolution operator with the weight function for Hartley integral transform. Several algebraic properties of this convolution operator are presented. In application, we apply this convolution operator to solving a class of integral equation and system of integral equations of Toeplitz plus Hankel type. On the other hand, we study the Watson- type integral transform for this convolution operator. We establish necessary and sufficient conditions for these operators to be unitary in the space and get their inverse represented in the conjungate symetric form. Moreover, we also formulate the Plancherel type theorem for aforementioned operators, prove a sequence of functions that converges to original function in the norm of and further show the boundedness of these operator. Finally, we study a class of integro- differential equation of Barashin type.

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