Tables of integrals

Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

Integral transforms and their applications

In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on \(L_{1}({\mathbb{R}})\), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.

/pdf/operational-properties-of-two-integral-transforms-of-fourier-55vgyllbmp.pdf

Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions

The solvability and explicit solutions of two integral equations via generalized convolutions

Integral Transforms of Fourier Cosine Convolution Type

A generalized convolution for the Fourier cosine and sine transforms is introduced its properties and applications to integral equations are considered

On the generalized convolutions for fourier cosine and sine transforms

A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

The generalized convolution with a weight function for the Fourier sine and cosine transforms is introduced. Its properties and applications to solving system of integral equations are considered.

On the generalized convolution with a weight function for the Fourier sine and cosine transforms

from Lp(R+) to Lq(R+), (1 6 p 6 2, p−1 + q−1 = 1) with the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form. Mathematics Subject Classification: 44A05, 44A35

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Integral transforms of the form
 f ( x ) ↦ g ( x ) = ( 1 − d 2 / d x 2 ) { ∫ 0 ∞ k 1 ( y ) [ f ( | x + y − 1 | ) + f ( | x − y + 1 | ) − f ( x + y + 1 ) − f ( | x − y − 1 | ) ] d y + ∫ 0 ∞ k 2 ( y ) [ f ( x + y ) + f ( | x − y | ) ] d y } from L p ( ℝ + ) to L q ( ℝ + ) , ( 1 ≤ p ≤ 2 , p − 1 + q − 1 = 1 ) are studied. Watson's and Plancherel's
theorems are obtained.

/pdf/integral-transforms-of-fourier-cosine-and-sine-generalized-10fxa5ymq2.pdf

Nguyen Xuan Thao

Papers

On the generalized convolutions for fourier cosine and sine transforms

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

On the generalized convolution with a weight function for the Fourier sine and cosine transforms

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type