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List Price:  $145.00 
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Hardcover ISBN:  9780821841143 
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Hardcover ISBN:  9780821841143 
Product Code:  ADVSOV/13 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 
eBook ISBN:  9781470446109 
Product Code:  ADVSOV/13.E 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 
Hardcover ISBN:  9780821841143 
eBook ISBN:  9781470446109 
Product Code:  ADVSOV/13.B 
List Price:  $290.00 $217.50 
MAA Member Price:  $261.00 $195.75 
AMS Member Price:  $232.00 $174.00 

Book DetailsAdvances in Soviet MathematicsVolume: 13; 1992; 210 ppMSC: Primary 20; 35; 47; 49; Secondary 16; 81; 90;
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.
ReadershipResearch mathematicians.

Table of Contents

Articles

S. Dobrokhotov, V. Kolokoltsov and V. Maslov — Quantization of the Bellman equation, exponential asymptotics and tunneling

P. Dudnikov — Endomorphisms of the semimodule of bounded functions

P. Dudnikov and S. Samborskii — Endomorphisms of finitely generated free semimodules

V. Kolokoltsov — On linear, additive, and homogeneous operators in idempotent analysis

S. Lesin and S. Samborskii — Spectra of compact endomorphisms

V. Maslov and S. Samborskii — Stationary HamiltonJacobi and Bellman equations (existence and uniqueness of solutions)

S. Samborskii and G. Shpiz — Convex sets in the semimodule of bounded functions

S. Samborskii and A. Tarashchan — The Fourier transform and semirings of Pareto sets

M. Shubin — Algebraic remarks on idempotent semirings and the kernel theorem in spaces of bounded functions

S. Yakovenko and L. Kontorer — Nonlinear semigroups and infinite horizon optimization


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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.
Research mathematicians.

Articles

S. Dobrokhotov, V. Kolokoltsov and V. Maslov — Quantization of the Bellman equation, exponential asymptotics and tunneling

P. Dudnikov — Endomorphisms of the semimodule of bounded functions

P. Dudnikov and S. Samborskii — Endomorphisms of finitely generated free semimodules

V. Kolokoltsov — On linear, additive, and homogeneous operators in idempotent analysis

S. Lesin and S. Samborskii — Spectra of compact endomorphisms

V. Maslov and S. Samborskii — Stationary HamiltonJacobi and Bellman equations (existence and uniqueness of solutions)

S. Samborskii and G. Shpiz — Convex sets in the semimodule of bounded functions

S. Samborskii and A. Tarashchan — The Fourier transform and semirings of Pareto sets

M. Shubin — Algebraic remarks on idempotent semirings and the kernel theorem in spaces of bounded functions

S. Yakovenko and L. Kontorer — Nonlinear semigroups and infinite horizon optimization