Paper's Title:

On the Integral Equations via Hartley Superconvolutions

Author(s):

Nguyen Minh Khoa

Department of Mathematics, Electric Power University,
Ha Noi,
Viet Nam.
E-mail: khoanm@epu.edu.vn

Abstract:

The new superconvolutions for the Hartley integral transforms are formulated and their properties are studied. Furthermore, we also formulate the Young type theorem for these superconvolutions in the function space L_s^αβγ(R) and get its norm estimations. We apply them to solve integral equations and system of integral equations of Toeplitz plus Hankel type.

Paper's Title:

On the Polyconvolution of Hartley Integral Transforms H₁, H₂, H₁ and Integral Equations

Author(s):

Nguyen Minh Khoa and Dau Xuan Luong

Department of Mathematics,
Electric Power University,
Ha Noi, and Faculty of Fundamental Science,
Ha Long University, Quang Ninh,
Viet Nam.
E-mail: khoanm@epu.edu.vn, dauxuanluong@gmail.com 

Abstract:

In this paper, we construct and study a new polyconvolution * (f,g,h)(x) of functions f, g, h. We will show that the polyconvolution satisfy the following factorization equality

H₁[*(f,g,h)](y)=(H₂f)(y)(H₁g)(y)(H₁h)(y), ∀y∈ R. 

We prove the existence of this polyconvolution in the space L(R). As examples, applications to solve an integral equation of polyconvolution type and two systems of integral equations of polyconvolution type are presented.

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