Product Formulas, Nonlinear Semigroups, and Addition of Unbounded Operators

Paul R. Chernoff

1974年1月 · American Mathematical Society: Memoirs of the American Mathematical Society 第 140 冊 · American Mathematical Soc.

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This work deals with the general theory, both linear and non-linear, of operator semigroup product formulas of the type lim [over] n[right arrow][infinity] F(t/n) [superscript]n = G(t). The principal application is the use of the Trotter-Lie product formula e [superscript]tC = lim [over] n[right arrow][infinity] (e [superscript]t/nA e [superscript]t/nB) [superscript]n to define a generalized addition of semigroup generators, and self-adjoint operators in particular. The properties of generalized addition, both regular and pathological, are discussed.