论文标题
双对运算符，单数非原子测量的谐波分析和Krein-Feller扩散
Dual pairs of operators, harmonic analysis of singular non-atomic measures and Krein-Feller diffusion
论文作者
论文摘要
我们表明，Krein-Feller操作员自然与固定的度量$μ$相关，假定为正，$σ$ -finite和非原子。引入了双对操作员，由两个希尔伯特空间携带，$ l^{2} \ left（μ\右）$和$ l^{2} \ left（λ\右）$，其中$λ$表示Lebesgue Measure。一个相关的操作员对由两个特定的密集定义（未结合）的操作员组成，每个操作员都包含在另一个操作员中。然后，这对相应的$ $ $ -KREIN-FELLER操作员作为可近距离的二次形式进行了严格的分析。作为一种应用，对于给定的度量$μ$，包括分形度量的情况，我们计算相关的扩散，半群，dirichlet形式和$ $ $ $ $ $ $ $ $ $ $ $ $ $。
We show that a Krein-Feller operator is naturally associated to a fixed measure $μ$, assumed positive, $σ$-finite, and non-atomic. Dual pairs of operators are introduced, carried by the two Hilbert spaces, $L^{2}\left(μ\right)$ and $L^{2}\left(λ\right)$, where $λ$ denotes Lebesgue measure. An associated operator pair consists of two specific densely defined (unbounded) operators, each one contained in the adjoint of the other. This then yields a rigorous analysis of the corresponding $μ$-Krein-Feller operator as a closable quadratic form. As an application, for a given measure $μ$, including the case of fractal measures, we compute the associated diffusion, semigroup, Dirichlet forms, and $μ$-generalized heat equation.
