Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics.
In this monograph, the...

This book is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions.

 

This book is comprised of two parts. The first part is devoted to the Riemann integral, and provides a novel approach, that are rarely found in other treatments of Riemann integration. The second part follows the approach of Riesz and Nagy in which the Lebesgue integral is developed without the need for any measure theory.