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All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-c

Holomorphic functions. --- Functional analysis. --- Convexity spaces. --- Convex surfaces. --- Complexes. --- Linear complexes --- Algebras, Linear --- Coordinates --- Geometry --- Line geometry --- Transformations (Mathematics) --- Convex areas --- Convex domains --- Surfaces --- Spaces, Convexity --- Convex sets --- Vector spaces --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functions, Holomorphic --- Functions of several complex variables