Dissipative Holomorphic Functions, Bloch Radii, and the Schwarz Lemma
نویسندگان
چکیده
The Hille-Yosida and Lumer-Phillips theorems play an important role in the theory of linear operators and its applications to evolution equations, probability and ergodic theory. (See, for example, [17] and [9].) Different nonlinear generalizations and analogues of these theorems can be found, for instance, in [13] and [2]. We are interested in establishing analogues of these theorems for the class of holomorphic functions which we view as a natural extension of the class of continuous linear operators. An analogue of the Hille-Yosida theorem for holomorphic functions was given in [14]. See also [15, 1]. Also, certain versions of the Hille-Yosida theorem as well as the Lumer-Phillips theorem were presented for nonlinear continuous operators in
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