Ordinary differential operators in Hilbert spaces and Fredholm pairs
Ordinary differential operators in Hilbert spaces and Fredholm pairs
复制标题
希尔伯特空间和 Fredholm 对中的普通微分算子
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Majer
中科院分区：
文献类型：
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作者：
Alberto Abbondandolo;P. Majer
抽象的。设A（t）是真实的Hilbert空间上的有界算子的一条路，该空间是在无穷远处双曲的.本文研究了算子F_A=d/dt-A（t）的Fredholm理论。我们将F_A的Fredholm性质与相应系统X^{prime}=A（t）X的稳定和不稳定线性空间联系起来。包括几个例子，指出相对于有限维的情况下，特别是关于谱流的作用的差异。我们定义了一个一般类的路径A的许多性质典型的有限维框架仍然保持。我们的动机是发展的线性理论，这是必要的设置莫尔斯同调希尔伯特流形。
Abstract. Let $A(t)$ be a path of bounded operators on a real Hilbert space, hyperbolic at $pm infty$. We study the Fredholm theory of the operator $F_A=d/dt-A(t)$. We relate the Fredholm property of $F_A$ to the stable and unstable linear spaces of the associated system $X^{prime}=A(t)X$. Several examples are included to point out the differences with respect to the finite dimensional case, in particular concerning the role of the spectral flow. We define a general class of paths A for which many properties typical of the finite dimensional framework still hold. Our motivation is to develop the linear theory which is necessary for the set-up of Morse homology on Hilbert manifolds.