2018
DOI: 10.1002/mma.5279
|View full text |Cite
|
Sign up to set email alerts
|

Integral equation of Toeplitz plus Hankel's type and parabolic equation related to the Kontorovich‐Lebedev‐Fourier generalized convolutions

Abstract: In this paper, we consider a class of integral equations with two Toeplitz plus Hankel's type kernels, and a class of parabolic equations. Using the Kontorovich‐Lebedev transform method, we obtain the closed form of solutions related to the Kontorovich‐Lebedev‐Fourier generalized convolutions. Furthermore, the estimate of solution in Lp with weight is established.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
4
0

Year Published

2020
2020
2023
2023

Publication Types

Select...
4

Relationship

3
1

Authors

Journals

citations
Cited by 4 publications
(4 citation statements)
references
References 12 publications
0
4
0
Order By: Relevance
“…and K2(x, τ ) = 1 2πx R + e −x cosh(τ −θ) + e −x cosh(τ +θ) h(θ)dθ, has been proven in [35]. However, the solution of (5.1) in closed-form for general case is still open.…”
Section: Some Applicationsmentioning
confidence: 99%
“…and K2(x, τ ) = 1 2πx R + e −x cosh(τ −θ) + e −x cosh(τ +θ) h(θ)dθ, has been proven in [35]. However, the solution of (5.1) in closed-form for general case is still open.…”
Section: Some Applicationsmentioning
confidence: 99%
“…From there, the authors use these results to solve in a closed form some classes of the differential equations (see Hong et al 6 and Tuan 7 ), and the convolution integral equations (see Tuan et al 8 and Yakubovich & Britvina 9 ). These above convolutions are also used to solve in a closed form some classes of integral equations of Fredholm (see Tuan and Hong 10,11 ) and Toeplitz plus Hankel's type with parabolic equation (see Tuan et al 12 ) and consider the boundedness solutions of these problems (see Tuan et al, 12,14 Hoang et al, 13 and van Anh & Thao 15 ). The limitation in Hong et al, 6 Tuan, 7 and Tuan et al 14 is that it cannot show the Plancherel-type theorem and the boundedness of Watson integral transform operator.…”
Section: Introductionmentioning
confidence: 99%
“…The solution in closed form of the equation In recent years, the equation (1.1) with Γ = [0, T ] and the kernel is a periodic function that has been studied by many authors (see [1] and references therein). In [8][9][10][11][13][14][15], the authors studied the equation (1.1) in case Γ = (0, +∞) and kernel is of the Toeplitz plus Hankel type.…”
Section: Introductionmentioning
confidence: 99%
“…However, we prove Theorems 3.1, 3.2, 4.1 and 4.2 by a method without using Wiener-Levy theorem. Tuan et al [13] studied the equation (1.1) with a kernel of the generalized convolution. It is harder to make function spaces of solution for the equation in Theorem 3.1, 3.2 if compared with results in [13].…”
Section: Introductionmentioning
confidence: 99%