Orthogonal PolynomialsElsevier, 2014 M05 17 - 294 páginas Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szego's theory. This book is useful for those who intend to use it as reference for future studies or as a textbook for lecture purposes |
Contenido
| 11 | |
Chapter 2 Elements of the Theory of the HamburgerStieltjes Momentum Problem | 54 |
Chapter 3 Quadrature Procedure and Interpolation over the Zeros of the Orthogonal Polynomials | 88 |
Chapter 4 Convergence Theory of the Series of Orthogonal Polynomials | 138 |
Chapter 5 The Theory of G Szegő | 187 |
Some unsolved problems | 273 |
| 279 | |
| 291 | |
| 293 | |
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A(du absolutely continuous absolutely convergent An(dx analytic asymptotic formula bounded variation Chebyshev polynomials coefficients condition consequence D(du denote doz(x dx(x dz(x equal estimate everywhere exists finite interval Fourier series function f(x furthermore gonal holds uniformly hypotheses of Theorem implies inequality infer inner subinterval interpolation Jacobi polynomials jump function Lebesgue Legendre polynomials Lemma Let Br(dx let x(x Ln(dx ln(x log|A(du m-distribution dx m-distribution function M(II Math momentum problem nomials non-decreasing non-negative obtain open unit circle orthogonal expansion orthogonal polynomials orthogonal series partial sums pn(a pn(dx points of discontinuity polynomial of degree positive proof of Theorem proved our statement quadrature formula radial limit value relation Riesz right-hand side S(dx satisfied show the validity Stieltjes integrable Suppose Szegó Theorem 2.1 tion Turán Uber uniform convergence uniformly with respect vanishes weight function zeros of pn(x