Algebraic properties of the new polyconvolution operator related to the Laplace, Fourier cosine integral transforms and applications

Iranian Journal of Numerical Analysis and Optimization

مقاله 9، دوره 17، Issue 1 - شماره پیاپی 40، بهار 2027، صفحه 247-272   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2026.99197.1889

نویسندگان

Khoa Nguyen Minh^* ؛ Le Trong Phuoc Bui؛ Van Thang Tran

Department of Mathematics, Electric Power University, 235 Hoang Quoc Viet, Nghia Do, Hanoi, Viet Nam.

چکیده

This work is focused on investigating a new polyconvolution operator with the trigonometric weight function $\beta(y_1)=\cos y_1$ associated with the Laplace and Fourier cosine integral transforms. We give an explicit form of this operator, prove the corresponding factorization identity, and establish some important algebraic properties of it, together with a Titchmarsh-type theorem. Within this analytic setting, we obtain fundamental properties including $L_1$-boundedness, Young-type inequalities on mixed $L_p$ spaces, and a norm inequality of Saitoh's type in the $L_p(\Rp,q_i)$ weight spaces. Applications demonstrate the operator's effectiveness in solving some new classes of integral equations of Toeplitz plus Hankel type and of polyconvolution type, a system of equations of polyconvolution type, and an integro-differential equation of Barbashin type, yielding explicit closed-form solutions.

کلیدواژه‌ها

Fourier cosine؛ Laplace integral transforms؛ Convolution؛ Generalized convolution؛ Polyconvolution؛ Integral equation؛ Integro-differential Barbashin equation