This book is a new edition of a titleoriginally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents thesein a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory.
The content of thefirst editionis still relevant, however the new edition will include several new results established after 1992; new text willcomprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques whichwill be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.
Keywords: reflecting rays; generalized geodesics; periodic geodesics; generic properties of periodic geodesics; length spectrum; Poisson relation; inverse spectral problems; scattering rays; scattering amplitude; inverse scattering problems, Applied Mathematics in Science, Mathematics Special Topics, Applied Mathematics in Science, Mathematics Special Topics