Articoli correlati a Spatial Algebras: Algebraic Foundations, Spectral Reconstruc...
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Spatial Algebras develops a new algebraic framework obtained by extending the complex plane with real idempotent directions while preserving the identity of each channel. The resulting structures are commutative and have an identity element, but they are generally nonassociative. Rather than treating nonassociativity merely as a defect, the book shows how the associator can be used to reconstruct spatial information lost under complex projection.
Beginning with the necessary foundations, the text first develops finite-dimensional spatial algebras and then extends the theory to infinite-dimensional families built over classical sequence spaces. Topics include multiplication operators, spectral theory, resolvents, functional calculus, coupled spectral representations, associator reconstruction, and Hilbertian geometry.
The theory is subsequently transported to bundles and dynamical systems, with discussions of projectors, connections, transfer between channels, curvature, symmetries, and bifurcation. The final part presents two advanced applications: Multichannel Spectral Geometry and a positive realization of Kaluza-Klein channels.
Designed for readers with an undergraduate degree in mathematics, the book is self-contained and requires no previous study of nonassociative algebras. Definitions are supported by conceptual preparation, detailed proofs, examples, counterexamples, graded exercises, and answers or hints. Clear warnings distinguish established results from open directions and delimit the mathematical scope of the physical applications.
This volume will be of interest to students, researchers, and instructors working in algebra, functional analysis, operator theory, spectral theory, differential geometry, and mathematical physics.
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Informazioni sull'autore
Kleber Soares Câmara holds a PhD in Mathematics from the Federal University of Paraíba and is a professor at the Federal Rural University of the Semi-Arid Region (UFERSA), Brazil. His academic work focuses on mathematical analysis, operator theory, spectral theory, nonassociative algebras, and their applications. He has taught undergraduate and graduate mathematics since 2012.
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Spatial Algebras: Algebraic Foundations, Spectral Reconstruction, and Applications (Paperback or Softback)
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Kleber Camara 9/12/2026, 2026
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Spatial Algebras : Algebraic Foundations, Spectral Reconstruction, and Applications
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Taschenbuch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Spatial Algebras develops a self-contained theory of commutative, unital, and generally nonassociative algebras that extend the complex numbers by adjoining real idempotent directions.The book begins with finite-dimensional spatial algebras and introduces their algebraic structure, associators, idempotents, multiplication operators, elementary functions, spectral coordinates, and functional calculus. It then develops an infinite-dimensional scale of spatial algebras, with detailed treatments of bounded multiplication operators, spectra, resolvents, reconstruction through associators, and the corresponding Hilbertian theory.The later chapters transport the algebraic decomposition to bundles, connections, curvature, dynamical systems, variational principles, symmetries, and bifurcation theory. Two advanced applications are presented separately: Multichannel Spectral Geometry and a heat-kernel-regularized realization of Kaluza-Klein channels. The mathematical scope and physical limitations of these applications are explicitly stated.Designed for advanced undergraduate students, graduate students, instructors, and researchers, the book includes definitions, complete proofs, examples, counterexamples, graded exercises, and an extensive chapter of answers and hints. It is suitable for readers interested in algebra, functional analysis, operator theory, spectral theory, differential geometry, and mathematical physics. Codice articolo 9786502363737
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Spatial Algebras | Algebraic Foundations, Spectral Reconstruction, and Applications
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Taschenbuch. Condizione: Neu. Spatial Algebras | Algebraic Foundations, Spectral Reconstruction, and Applications | Kleber Câmara | Taschenbuch | Englisch | 2026 | Kleber Câmara | EAN 9786502363737 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand. Codice articolo 138047183
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