Formulas in inverse and ill-posed problems (Q1358977)

This book is devoted mainly to the results of the author and his collaborators with emphasis on (explicit) solutions of inverse problems given by formulas. In Chapters 1 and 2 there is a (somehow formal) approach to inverse problems for evolution equations (via Fourier transform with no convergence conditions). Chapter 3 contains useful formulae for the classical inverse kinematic problem. Chapter 4 discusses integral geometry and is a valuable addition to, say, the book of \textit{F. Natterer} [The mathematics of computerized tomography, Teubner and Wiley (1986; Zbl 0617.92001)]. In particular, a stability estimate is given when a function is determined from its integrals over spheres of variable radii and a uniqueness theorem about simultaneous identification of several functions from standard data of integral geometry is obtained. Chapter 5 contains several examples of functions solving inverse problems. Concluding, Chapter 6 describes models in biology and sociology, for example, an equation in convolutions is suggested to describe a density of ethnic distribution.