Orthogonal FunctionsR. E. Krieger Publishing Company, 1959 - 411 pages Highly regarded treatise contains a rich compilation of general results and convenient criteria concerning Fourier series, Legendre series, Laguerre and Hermite polynomials. Until publication of this book, much of the material had not been available in English. First paperback edition. Translated by Ainsley H. Diamond. Foreword. Bibliography. 14 black-and-white illustrations. |
Table des matières
Expansion in Series of Orthogonal Functions and Preliminary | 1 |
Elementary Notions of Hilbert Space | 7 |
Convergence in the Mean | 13 |
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Expressions et termes fréquents
² dt a₁ b₂ bounded variation coefficients consequently constant continuous converges uniformly cos y cos² defined denote differential e-x² equation f(cos f₁ f₂ finite interval finite measure fn(t following theorem formula Fourier series function f(x H₂(x Hermite Hermite polynomials Hn(x inequality integrable in g interval interior J. V. Uspensky Laguerre Laplace series Legendre polynomials Legendre series Let f(x linearly independent Math multiplying obtain orthogonal orthonormal P(cos P₁ P₂ P₂(x Pn(x pointwise convergence positive number Proof prove respect right side satisfies sequence series of f(x sin½ sin² Sn(x spherical harmonics Stieltjes summability uniformly convergent vanishes whence x)dx zero Απ π π Σα ди дф