Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.
This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Bessel Functions and Fourier-Bessel Series, and the Eigenfunction Method and its Applications to Mathematical Physics. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text. Richard Silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering. He has also added a bibliography, containing suggestions for collateral and supplementary reading. 1962 edition.
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TRIGONOMETRIC FOURIER SERIES
CONVERGENCE OF TRIGONOMETRIC FOURIER SERIES
TRIGONOMETRIC SERIES WITH DECREASING COEFFICIENTS
OPERATIONS ON FOURIER SERIES
SUMMATION OF TRIGONOMETRIC FOURIER SERIES
DOUBLE FOURIER SERIES THE FOURIER INTEGRAL
BESSEL FUNCTIONS AND FOURIERBESSEL SERIES
THE EIGENFUNCTION METHOD AND ITS APPLICATIONS TO MATHEMATICAL PHYSICS
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absolutely integrable derivative absolutely integrable function apply arithmetic means Bessel Functions Bessel's equation Bessel's inequality boundary conditions boundary value problem bounded consider const constant continuous function converges uniformly cosine eigenfunctions eigenvalues Example exists expansion extension of/(x finite number follows Fourier coefficients Fourier series Fourier-Bessel series function defined function of period gives graph Heat Flow hence implies initial conditions integrable function f(x Jp(x lemma Let f(x membrane mx dx nodal lines number of points nx dx obviously odd function orthogonal system partial sums particular solutions period 2n periodic extension piecewise smooth piecewise smooth function point of discontinuity Proof prove result satisfies the boundary satisfy the condition series converges sin2 smooth function square integrable function string sufficiently large term by term term differentiation that/(x theorem of Sec trigonometric series trigonometric system uniformly convergent vanishes vectors whole x-axis
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