Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals
Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals
复制标题
由凸泛函的次微分生成的非线性半群的 Trotter 乘积公式
DOI：
10.2969/jmsj/03010169
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发表时间：
1978
影响因子：
0.7
通讯作者：
K. Masuda
中科院分区：
文献类型：
--
作者：
Tosio Kato;K. Masuda
whenever $A_{1},$ $A_{2}$ are nonnegative selfadjoint operators in a Hilbert space $H$ (with no restriction on their domains). Here $P^{\prime}$ is the orthogonal projection of $H$ onto the subspace $H^{\prime}$ spanned by $D^{\prime}=D(A_{1}^{1/2})\cap D(A_{2}^{1/2})$ and $A^{\prime}$ is the form sum of $A_{1},$ $A_{2}(i$ . $e$ . the selfadjoint operator in $H^{\prime}$ associated with the denselydefined, closed quadratic form $\Vert A_{1}^{1/2}u\Vert^{2}+\Vert A_{2}^{1/2}u\Vert^{2}$). The purpose of the present paper is to prove a nonlinear analogue of (1.1). As a natural generalization of a nonnegative selfadjoint operator, $A_{j}$ will be replaced by the subdifferential $\partial\varphi_{j}$ of a lower semicontinuous, convex function
whenever $A_{1},$ $A_{2}$ are nonnegative selfadjoint operators in a Hilbert space $H$ (with no restriction on their domains). Here $P^{\prime}$ is the orthogonal projection of $H$ onto the subspace $H^{\prime}$ spanned by $D^{\prime}=D(A_{1}^{1/2})\cap D(A_{2}^{1/2})$ and $A^{\prime}$ is the form sum of $A_{1},$ $A_{2}(i$ . $e$ . the selfadjoint operator in $H^{\prime}$ associated with the denselydefined, closed quadratic form $\Vert A_{1}^{1/2}u\Vert^{2}+\Vert A_{2}^{1/2}u\Vert^{2}$). The purpose of the present paper is to prove a nonlinear analogue of (1.1). As a natural generalization of a nonnegative selfadjoint operator, $A_{j}$ will be replaced by the subdifferential $\partial\varphi_{j}$ of a lower semicontinuous, convex function