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The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

机译：Delsarte的Gelfand-Levitan-marchenko型方程的结构线性多维微分算子的嬗变算子和操作员铅笔。第1部分

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摘要

An analog of Gelfand-Levitan-Marchenko integral equations for multi-dimensional Delsarte transmutation operators is constructed by means ofstudying their differential-geometric structure based on the classical Lagrangeidentity for a formally conjugated pair of differential operators. An extensionof the method for the case of affine pencils of differential operators issuggested.

机译：通过研究形式共轭对差分算子对的经典Lagrange恒等性，研究多维Delsarte mut变算子的Gelfand-Levitan-Marchenko积分方程的类似物。建议对微分算子的仿射铅笔方法进行扩展。

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Golenia, J.; Prykarpatsky, A. K.; Prykarpatsky, Y. A.;
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年度 2004
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专利

1. Generalized de Rham-Hodge theory of multidimensional Delsarte transmutations of differential operators and its applications for nonlinear dynamic systems [J] . Bogolyubov NN, Prykarpatsky YA, Samoilenko AM, Physics of particles and nuclei . 2005,第Suppla1期

机译：差分运算符多维Delsarte传输的广义de rham-hodge理论及其对非线性动力系统的应用
2. The spectral and differential geometric aspects of a generalized De Rham-Hodge theory related with Delsarte transmutation operators in multidimension and its applications to spectral and soliton problems [J] . Samoilenko AM, Prykarpatsky YA, Prykarpatsky AK Nonlinear Analysis: An International Multidisciplinary Journal . 2006,第2期

机译：与多维Delsarte d变算子相关的广义De Rham-Hodge理论的谱和微分几何方面及其在谱和孤子问题中的应用
3. Transmutation operators associated with a dunkl type differential-difference operator on the real line and certain of their applications [J] . Mohamed Ali Mourou Integral transforms and special functions . 2001,第1期

机译：与实线上的dunkl型微分差分算子相关的变换算子及其某些应用
4. Fractional order differential and integral equations with Erdélyi‐Kober operators: Explicit solutions by means of the transmutation method [C] . Virginia S. Kiryakova International Conference "Applications of Mathematics in Engineering and Economics" . 2011

机译：与Erdélyi-kober运算符的分数级差分和整体方程：通过嬗变方法显式解决方案
5. Numerical solution of linear transport equations with scattering operators of integral and differential type. [D] . Phillips, Kevin Gregory. 2008

机译：具有积分和微分类型散射算子的线性传输方程的数值解。
6. Some Linear Operators in the Theory of Partial Differential Equations [O] . S. Bergman, M. Schiffer 1950

机译：偏微分方程理论中的一些线性算子
7. Differential-geometric and topological structure of multidimensional Delsarte transmutation operators [O] . Prykarpatsky, Yarema, Samoilenko, Anatoliy, Prykarpatsky, Anatoliy K. 2004

机译：多维的微分几何和拓扑结构 Delsarte嬗变运算符
8. Note on Gegenbauer's Differential Operators and Their Applications to Linear Differential Equations [R] . Onyango-Otieno, V. P. 1985

机译：关于Gegenbauer微分算子及其在线性微分方程中应用的注记

The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

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