Idempotent analysis is a new branch of mathematical analysis concerned with functional spaces and their mappings when the algebraic structure is generated by an idempotent operation. The articles in this collection show how idempotent analysis is playing a unifying role in many branches of mathematics related to external phenomena and structures-a role similar to that played by functional analysis in mathematical physics, or numerical methods in partial differential equations. Such a unification necessitates study of the algebraic and analytic structures appearing in spaces of functions with values in idempotent semirings. The papers collected here constitute an advance in this direction.
Idempotent analysis (in place of an introduction) by V. P. Maslov and S. N. Samborskii Quantization of the Bellman equation, exponential asymptotics and tunneling by S. Yu. Dobrokhotov, V. N. Kolokoltsov, and V. P. Maslov Endomorphisms of the semimodule of bounded functions by P. I. Dudnikov Endomorphisms of finitely generated free semimodules by P. I. Dudnikov and S. N. Samborskii On linear, additive, and homogeneous operators in idempotent analysis by V. N. Kolokoltsov Spectra of compact endomorphisms by S. A. Lesin and S. N. Samborskii Stationary Hamilton-Jacobi and Bellman equations (existence and uniqueness of solutions) by V. P. Maslov and S. N. Samborskii Convex sets in the semimodule of bounded functions by S. N. Samborskii and G. B. Shpiz The Fourier transform and semirings of Pareto sets by S. N. Samborskii and A. A. Tarashchan Algebraic remarks on idempotent semirings and the kernel theorem in spaces of bounded functions by M. A. Shubin Nonlinear semigroups and infinite horizon optimization by S. Yu. Yakovenko and L. A. Kontorer.