Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.
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ISBN-13
978-0-387-97901-4 (9780387979014)
DOI
10.1007/978-1-4612-2966-7
Schweitzer Klassifikation
Difference Hypergeometric Functions.- Padé Approximants for Some q-Hypergeometric Functions.- Summation Theorems for Basic Hypergeometric Series of Schur Function Argument.- Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures.- Szeg? Type Asymptotics for Minimal Blaschke Products.- Asymptotics of Hermite-Padé Polynomials.- On the Rate of Convergence of Padé Approximants of Orthogonal Expansions.- Spurious Poles in Diagonal Rational Approximation.- Expansions for Integrals Relative to Invariant Measures Determined by Contractive Affine Maps.- Approximation of Measures by Fractal Generation Techniques.- Nonlinear Wavelet Approximation in the Space C (Rd).- Completeness of Systems of Translates and Uniqueness Theorems for Asymptotically Holomorphic Functions.- Approximation by Entire Functions and Analytic Continuation.- Quasi-Orthogonal Hilbert Space Decompositions and Estimates of Univalent Functions. II.- On the Differential Properties of the Rearrangements of Functions.- A Class of I.M. Vinogradov's Series and Its Applications in Harmonic Analysis.- A Lower Bound for the de Bruijn-Newman Constant ?. II.- On the Denseness of Weighted Incomplete Approximations.- Asymptotics of Weighted Polynomials.
