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学校代码：10213
密级：公开
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理学硕士学位论文
解剖映射的基本性质
硕 士 研 究 生：张蕾
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导
师：李容录教授
42essor Li Ronglu established the new three basic principles for
three very large families of mappings respectively. Each of the three families of
mappings includes all linear mappings handled in the classical principles. Meanwhile,
the family of dissecting mappings given by Professor Li is used to develop the theory
of distributions. He also estiblishes a new pan-linear distribution theory. The
theoretical value and field of applications of functional analusis are promoted and
expanded to a new level. Based on the existing properties of dissecting mappings,
this paper does some in-depth study of the dissecting mappings and gives several
new properties.
Firstly, the paper presents the continuous properties of dissecting mappings,
points out that the dissecting mappings are continuous when and only when they are
continuous in zero.
Secondly, the paper improves an original sufficient and necessary condition for
the dissecting mappings f : ¡ ® ¡ , makes it link with the Lipschitz condition. We
further study the structure of dissecting mappings, and points out the stong
dissecting mappings are Lipschitz.
Again, we define the norm on the dissecting mappings, and give the properties
of the norm.
Finally, this paper also studies the properties of the conjugate operator of
dissecting mapping, points out the conjugate operator is linear.
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Keywords
dissecting mappings, continuous, norm, conjugate operator
II
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XX工业大学理学硕士学位论文
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目
录
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摘
要.................................................................................................................. I
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ABSTRACT............................................................................................................ II
第 1 章 绪 论 .......................................................................................................