共查询到20条相似文献,搜索用时 566 毫秒
1.
Ts. E. Terdzhyan A. Kh. Khachatryan 《Computational Mathematics and Mathematical Physics》2009,49(4):691-697
One system of integral convolution equations is considered on a half-line with an noninvertible matrix integral operator whose symbol has a fourth-order zero. The application of a special factorization method makes it possible to distinguish noninvertible factors in the original noninvertible operator and reduce the system to a new system with a nonsingular integral operator. The structural theorem of the existence of a solution to the original system is proved. 相似文献
2.
3.
Nguyen Xuan Thao Hoang Thi Van Anh 《Mathematical Methods in the Applied Sciences》2014,37(15):2308-2319
In this paper, we construct and study a new generalized convolution (f * g)(x) of functions f,g for the Hartley (H1,H2) and the Fourier sine (Fs) integral transforms. We will show that these generalized convolutions satisfy the following factorization equalities: We prove the existence of this generalized convolution on different function spaces, such as . As examples, applications to solve a type of integral equations and a type of systems of integral equations are presented. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
Victor P. Palamodov 《Mathematische Nachrichten》1998,196(1):167-188
New reconstruction formula for the line integral transformation in Euclidean spaces is found. The general k-plane integral transform in Euclidean space is related to a totally geodesic integral transform for an arbitrary Riemannian space of constant curvature by means of a factorization property. Duality theorems for the totally geodesic transforms are stated. 相似文献
5.
Mircea Predeleanu 《Applied Mathematical Modelling》1984,8(6):378-382
Biot's consolidation theory is extended to a general class of viscoelastic bodies defined by Riemann-Stieltjes integral convolutions. From a new reciprocity theorem, proved for the governing equations including the inertia terms, the basic integral representations of the displacement fields and pore pressure are obtained. It is shown that, in the absence of internal inputs, a formulation of the dynamic problem in terms of the boundary unknown fields only is possible. 相似文献
6.
Localized boundary‐domain singular integral equations of Dirichlet problem for self‐adjoint second‐order strongly elliptic PDE systems 下载免费PDF全文
O. Chkadua S. E. Mikhailov D. Natroshvili 《Mathematical Methods in the Applied Sciences》2017,40(6):1817-1837
The paper deals with the three‐dimensional Dirichlet boundary value problem (BVP) for a second‐order strongly elliptic self‐adjoint system of partial differential equations in the divergence form with variable coefficients and develops the integral potential method based on a localized parametrix. Using Green's representation formula and properties of the localized layer and volume potentials, we reduce the Dirichlet BVP to a system of localized boundary‐domain integral equations. The equivalence between the Dirichlet BVP and the corresponding localized boundary‐domain integral equation system is studied. We establish that the obtained localized boundary‐domain integral operator belongs to the Boutet de Monvel algebra. With the help of the Wiener–Hopf factorization method, we investigate corresponding Fredholm properties and prove invertibility of the localized operator in appropriate Sobolev (Bessel potential) spaces. Copyright © 2016 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd. 相似文献
7.
V. Vol'kovich 《Journal of Theoretical Probability》1992,5(3):417-430
The notion of stochastic convolution arises from a study on various operations on probability measures. Although these operations appear in diverse branches of mathematics, their properties turn out to be similar. A general model for the study of such convolutions has been provided in earlier papers by the author. In this paper we consider some new properties of this model for convolutions corresponding to generalized integral transforms. The tools of this model can be applied to study many realizations of stochastic convolutions, for example, Urbanik's regular convolutions, the polynomial hypergroup's convolutions of Lasser, the convolution of Askey-Gasper and Levitan's convolution. 相似文献
8.
Ding-dong Gong 《高校应用数学学报(英文版)》2008,23(3):273-278
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well. 相似文献
9.
A method of explicit factorization of matrix functions of second order is proposed. The method consists of reduction of this problem to two scalar barrier problems and a finite system of linear equations. Applications to various classes of singular integral equations and equations with Toeplitz and Hankel matrices are given. 相似文献
10.
1 IntroductionSillce tl1e limit value fOrlnula, viz. tl1e Plemelj fOrn1ula, of the Cauthe type integraJ withBochner-Martinelli kernel was proved in 1957[1], it has beell successfully used to the study Ofsingular i1ltegral equatious, solvi11g the 0b--equation, holomorphic extension, 0--closed exten-sion and C-R 111al1ifolds[2-51. Evideutly, the researcl1 of higher order singular integrals withBochuer-Martinelli kerllel itself also l1as important significallce. In 1952, J. Hadanmrd firstde… 相似文献
11.
12.
Farrukh Mukhamedov Otabek Khakimov Ahmad Fadillah Embong 《Mathematical Methods in the Applied Sciences》2020,43(15):9102-9118
In the present paper, we consider integral equations, which are associated with nonlinear Markov operators acting on an infinite-dimensional space. The solvability of these equations is examined by investigating nonlinear Markov operators. Notions of orthogonal preserving and surjective nonlinear Markov operators defined on infinite dimension are introduced, and their relations are studied, which will be used to prove the main results. We show that orthogonal preserving nonlinear Markov operators are not necessarily satisfied surjective property (unlike finite case). Thus, sufficient conditions for the operators to be surjective are described. Using these notions and results, we prove the solvability of Hammerstein equations in terms of surjective nonlinear Markov operators. 相似文献
13.
Bui Thi Giang Nguyen Van Mau Nguyen Minh Tuan 《Integral Equations and Operator Theory》2009,65(3):363-386
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
L1(\mathbbR)L_{1}({\mathbb{R}}), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel. 相似文献
14.
1.引言由于对积分算子方程来说,配置法比Galerkin法具计算量小的优点(少算一重积分),故配置法更受人们重视.但已有的文献几乎都是将配置空间取作非连续的分片多项式样条空间,以得到某种超收敛结果(如[1,2]).这种方法存在下列不足:(a)光滑核Volterra积分方程与光滑核Fredholm积分方程具完全不同的收敛性质[1],且需用不同的方法获得其加速收敛结果(比较[31与[4]),尽管Volterra积分方程在理论上被看作是Fredholm积分方程的特殊情形;(b)光滑核Volterra积分方程的配置解不具任何超收敛性,其迭代配置解也只在结点… 相似文献
15.
E. N. Mikhalkin 《Siberian Mathematical Journal》2006,47(2):301-306
We obtain an integral formula for a solution to a general algebraic equation. In this formula the integrand is an elementary function and integration is carried out over an interval. The advantage of this formula over the well-known Mellin formula is that the integral has a broader convergence domain. This circumstance makes it possible to describe the monodromy of a solution for trinomial equations. 相似文献
16.
刘春根 《数学物理学报(B辑英文版)》1996,(1)
TWO-DIMENSIONALSINGULARINTEGRALEQUATIONSOFTHEHYPERCOMPLEXFUNCTIONS(刘春根)¥LiuChangen(Dept.ofMathNankaiUniv.,Tianjin50071,China.... 相似文献
17.
A. Kh. Khachatryan Ts. E. Terjiyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(5):296-301
The paper studies the Wiener-Hopf equations with kernels representable as superposition of complex-valued exponents. Such kernels arise in the kinetic gas theory, in the radiation transfer, etc. By application of a special, three-factor expansion of the initial uninvertible operator, the solution of the considered equation is reduced to those of two simple Volterra equations and a Wiener-Hopf integral equation with a contractive operator. A structural existence theorem is proved. 相似文献
18.
In this paper we develop and analyze a bootstrapping algorithm for the extraction of potentials and arbitrary derivatives of the Cauchy data of regular three-dimensional second order elliptic boundary value problems in connection with corresponding boundary integral equations. The method rests on the derivatives of the generalized Green's representation formula, which are expressed in terms of singular boundary integrals as Hadamard's finite parts. Their regularization, together with asymptotic pseudohomogeneous kernel expansions, yields a constructive method for obtaining generalized jump relations. These expansions are obtained via composition of Taylor expansions of the local surface representation, the density functions, differential operators and the fundamental solution of the original problem, together with the use of local polar coordinates in the parameter domain. For boundary integral equations obtained by the direct method, this method allows the recursive numerical extraction of potentials and their derivatives near and up to the boundary surface.
19.
In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu. 相似文献
20.
Arcadii Z. Grinshpan 《Integral Equations and Operator Theory》2013,75(2):165-185
The recent work on discrete inequalities with the binomially made weights leads to a sharp weighted norm inequality for convolutions of complex-valued functions on a finite interval. This result and the Hadamard-type modifications of power series provide the basis for an integral approach to solution-kernel estimates for Volterra convolution equations and for various integro-differential and special function applications. The development of this approach and the new weighted norm inequalities for linear differential operators and generalized hypergeometric functions are presented in this paper. 相似文献