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Idempotent Analysis
Edited by: V. P. Maslov and S. N. Samborskiĭ
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Advances in Soviet Mathematics
1992; 210 pp; hardcover
Volume: 13
ISBN-10: 0-8218-4114-9
ISBN-13: 978-0-8218-4114-3
List Price: US$131
Member Price: US$104.80
Order Code: ADVSOV/13
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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.

Readership

Research mathematicians.

Table of Contents

  • V. P. Maslov and S. N. Samborskiĭ -- Idempotent analysis (in place of an introduction)
  • S. Yu. Dobrokhotov, V. N. Kolokoltsov, and V. P. Maslov -- Quantization of the Bellman equation, exponential asymptotics and tunneling
  • P. I. Dudnikov -- Endomorphisms of the semimodule of bounded functions
  • P. I. Dudnikov and S. N. Samborskiĭ -- Endomorphisms of finitely generated free semimodules
  • V. N. Kolokoltsov -- On linear, additive, and homogeneous operators in idempotent analysis
  • S. A. Lesin and S. N. Samborskiĭ -- Spectra of compact endomorphisms
  • V. P. Maslov and S. N. Samborskiĭ -- Stationary Hamilton-Jacobi and Bellman equations (existence and uniqueness of solutions)
  • S. N. Samborskiĭ and G. B. Shpiz -- Convex sets in the semimodule of bounded functions
  • S. N. Samborskiĭ and A. A. Tarashchan -- The Fourier transform and semirings of Pareto sets
  • M. A. Shubin -- Algebraic remarks on idempotent semirings and the kernel theorem in spaces of bounded functions
  • S. Yu. Yakovenko and L. A. Kontorer -- Nonlinear semigroups and infinite horizon optimization
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