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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Semigroups in Geometrical Function Theory (Paperback, Softcover reprint of hardcover 1st ed. 2001)
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Semigroups in Geometrical Function Theory (Paperback, Softcover reprint of hardcover 1st ed. 2001)
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Historically, complex analysis and geometrical function theory have
been inten sively developed from the beginning of the twentieth
century. They provide the foundations for broad areas of
mathematics. In the last fifty years the theory of holomorphic
mappings on complex spaces has been studied by many mathemati cians
with many applications to nonlinear analysis, functional analysis,
differential equations, classical and quantum mechanics. The laws
of dynamics are usually presented as equations of motion which are
written in the abstract form of a dy namical system: dx / dt + f (
x) = 0, where x is a variable describing the state of the system
under study, and f is a vector function of x. The study of such
systems when f is a monotone or an accretive (generally nonlinear)
operator on the under lying space has been recently the subject of
much research by analysts working on quite a variety of interesting
topics, including boundary value problems, integral equations and
evolution problems (see, for example, [19, 13] and [29]). In a
parallel development (and even earlier) the generation theory of
one parameter semigroups of holomorphic mappings in en has been the
topic of interest in the theory of Markov stochastic processes and,
in particular, in the theory of branching processes (see, for
example, [63, 127, 48] and [69]).
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