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An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Fourier series. --- Fourier series --- 517.518.4 --- 517.518.5 --- 517.51 --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- 517.518.5 Theory of the Fourier integral --- Theory of the Fourier integral --- 517.51 Functions of a real variable. Real functions --- Functions of a real variable. Real functions --- 517.518.4 Trigonometric series --- Acqui 2006

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This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate analysis, including approximations and numerical integration. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball, or those of Gaussian type, for which fairly explicit formulae exist. The approach is a blend of classical analysis and symmetry-group-theoretic methods. Reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers.

Orthogonal polynomials. --- Functions of several real variables. --- Real variables --- Several real variables, Functions of --- Functions of real variables --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Functions of several real variables --- Orthogonal polynomials --- 517.518 --- 517.518 Metric theory of functions --- Metric theory of functions --- Mathematical analysis