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This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Mathematics. --- Harmonic analysis. --- Applied mathematics. --- Engineering mathematics. --- Visualization. --- Abstract Harmonic Analysis. --- Applications of Mathematics. --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Engineering --- Engineering analysis --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Math --- Science

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This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject’s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality. Key features include: • a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory;  • over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance; • an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them.   Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course.     .

Mathematics. --- Computer science --- Algebra. --- Matrix theory. --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Applications of Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Appl.Mathematics/Computational Methods of Engineering. --- Math Applications in Computer Science. --- Computer science. --- Mathematical and Computational Engineering. --- Informatics --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Math --- Computer science—Mathematics. --- Games, Theory of --- Theory of games --- Mathematical models --- Algebras, Linear. --- Algebras, Linear --- Algebras, Linear - Problems, exercises, etc.