Orthogonal Functions Moment Theory and Continued Fractions Lecture Notes in Pure and Applied Mathematics Series

"Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."

Chebyshev-Laurent polynomials and weighted approximation; natural solutions of indeterminate strong Stieltjes moment problems derived from PC-fractions; a class of indeterminate strong Stieltjes moment problems with discrete distributions; symmetric orthogonal L-polynomials in the complex plane; continued fractions and orthogonal rational functions; interpolation of Nevanlinna functions by rationals with poles on the real line; symmetric orthogonal Laurent polynomials; interpolating Laurent polynomials; computation of the gamma and Binet functions by Stieltjes continued fractions; formulas for the moments of some strong moment distributions; orthogonal Laurent polynomials of Jacobi, Hermite and Laguerre types; regular strong Hamburger moment problems; asymptotic behaviour of the continued fraction coefficients of a class of Stieltjes transforms, including the Binet function; uniformity and speed of convergence of complex continued fractions K(an/1); separation theorem of Chebyshev-Markov-Stieltjes type for Laurent polynomials orthogonal on (0, alpha); orthogonal polynomials associated with a non-diagonal Sobolev inner product with polynomial coefficients; remarks on canonical solutions of strong moment problems; Sobolev orthogonality and properties of the generalized Laguerre polynomials; a combination of two methods in frequency analysis -the R(N)-process; zeros of Szego polynomials used in frequency analysis; some probabilistic remarks on the boundary version of Worpitzky's theorem.

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