| 一类带位移的奇异积分方程Noether条件与指数 |
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| 引用本文： | 林益. 一类带位移的奇异积分方程Noether条件与指数[J]. 华中科技大学学报(自然科学版), 1989, 0(1) |
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| 作者姓名： | 林益 |
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| 作者单位： | 华中理工大学数学系 |
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| 摘 要： | 本文讨论带有一般位移和未知函数复共轭值的奇异积分方程的Noether可解条件与指数公式。在反位移时,方程的Noether性归结为简单的非积分算子的同类问题;在正位移时,方程的Noether性归结为文献[1]中带一般位移的奇异积分方程的同类问题。方程的指数公式通过构造Noether算子连续族,利用同伦性质得到,它既与位移性质有关,又与位移不动点性质有关。
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| 关 键 词： | 位移算子 复共轭算子 奇异积分算子 诺特方程 逆算子定理 |
The Noether Condition and Index Formula for a Kind of Singular Integral Equations with Displacement |
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| Lin Yi. The Noether Condition and Index Formula for a Kind of Singular Integral Equations with Displacement[J]. JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE, 1989, 0(1) |
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| Authors: | Lin Yi |
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| Abstract: | In the book entitled "Singular Integral Equation with Displacement and Boundary Value Problem" by r. C. a discussion is made on the Noether property and index formula of Carleman's singular integral equations with displacement and complex conjugate value of unknown function in space Lp(). Under the condition of general displacement, the same problem is dealt with but without the restriction of Carleman's displacement and the expression is given;It is shown that the Noether condition and index formula depend on both the displacement property and the fixed point property of displacement. |
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| Keywords: | Displacement operator Complex conjugate operator Singular integral operator Noether equation The index of Noether equation |
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