I-Smooth Analysis: Theory And Applications

The edition introduces a new class of invariant derivatives and shows their relationships with other derivatives, such as the Sobolev generalized derivative and the generalized derivative of the distribution theory. This is a new direction in mathematics.

i-Smooth analysis is the branch of functional analysis that considers the theory and applications of the invariant derivatives of functions and functionals. The important direction of i-smooth analysis is the investigation of the relation of invariant derivatives with the Sobolev generalized derivative and the generalized derivative of distribution theory.

Until now, i-smooth analysis has been developed mainly to apply to the theory of functional differential equations, and the goal of this book is to present i-smooth analysis as a branch of functional analysis. The notion of the invariant derivative (i-derivative) of nonlinear functionals has been introduced in mathematics, and this in turn developed the corresponding i-smooth calculus of functionals and showed that for linear continuous functionals the invariant derivative coincides with the generalized derivative of the distribution theory. This book intends to introduce this theory to the general mathematics, engineering, and physicist communities.

Dr. A.V. Kim, PhD, is the head of the research group of the Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural Branch). He graduated from the mathematics department at Ural State University in 1980, received his doctorate from Ural State University in 1987, and received his Doctor of Science degree with his research monograph, Some problems of Functional Differential Equations theory, at the Institute of Mathematics and Mechanics in 2001. Before doing his research at the Russian Academy of Natural Science, he taught at the Seoul National University in the School of Electrical Engineering.