Ebook: Progress in Approximation Theory: An International Perspective

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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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 Szeg? type asymptotics and connections with Jacobi matrices; the convergence theory for Pad? and Hermite-Pad? 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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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 Szeg? type asymptotics and connections with Jacobi matrices; the convergence theory for Pad? and Hermite-Pad? 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.
Content:
Front Matter....Pages i-xviii
Difference Hypergeometric Functions....Pages 1-35
Pad? Approximants for Some q-Hypergeometric Functions....Pages 37-50
Summation Theorems for Basic Hypergeometric Series of Schur Function Argument....Pages 51-77
Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures....Pages 79-104
Szeg? Type Asymptotics for Minimal Blaschke Products....Pages 105-126
Asymptotics of Hermite-Pad? Polynomials....Pages 127-167
On the Rate of Convergence of Pad? Approximants of Orthogonal Expansions....Pages 169-190
Spurious Poles in Diagonal Rational Approximation....Pages 191-213
Expansions for Integrals Relative to Invariant Measures Determined by Contractive Affine Maps....Pages 215-239
Approximation of Measures by Fractal Generation Techniques....Pages 241-260
Nonlinear Wavelet Approximation in the Space C(R d )....Pages 261-283
Completeness of Systems of Translates and Uniqueness Theorems for Asymptotically Holomorphic Functions....Pages 285-293
Approximation by Entire Functions and Analytic Continuation....Pages 295-313
Quasi-Orthogonal Hilbert Space Decompositions and Estimates of Univalent Functions. II....Pages 315-331
On the Differential Properties of the Rearrangements of Functions....Pages 333-352
A Class of I.M. Vinogradov’s Series and Its Applications in Harmonic Analysis....Pages 353-402
A Lower Bound for the de Bruijn-Newman Constant ?. II....Pages 403-418
On the Denseness of Weighted Incomplete Approximations....Pages 419-429
Asymptotics of Weighted Polynomials....Pages 431-451

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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 Szeg? type asymptotics and connections with Jacobi matrices; the convergence theory for Pad? and Hermite-Pad? 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.
Content:
Front Matter....Pages i-xviii
Difference Hypergeometric Functions....Pages 1-35
Pad? Approximants for Some q-Hypergeometric Functions....Pages 37-50
Summation Theorems for Basic Hypergeometric Series of Schur Function Argument....Pages 51-77
Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures....Pages 79-104
Szeg? Type Asymptotics for Minimal Blaschke Products....Pages 105-126
Asymptotics of Hermite-Pad? Polynomials....Pages 127-167
On the Rate of Convergence of Pad? Approximants of Orthogonal Expansions....Pages 169-190
Spurious Poles in Diagonal Rational Approximation....Pages 191-213
Expansions for Integrals Relative to Invariant Measures Determined by Contractive Affine Maps....Pages 215-239
Approximation of Measures by Fractal Generation Techniques....Pages 241-260
Nonlinear Wavelet Approximation in the Space C(R d )....Pages 261-283
Completeness of Systems of Translates and Uniqueness Theorems for Asymptotically Holomorphic Functions....Pages 285-293
Approximation by Entire Functions and Analytic Continuation....Pages 295-313
Quasi-Orthogonal Hilbert Space Decompositions and Estimates of Univalent Functions. II....Pages 315-331
On the Differential Properties of the Rearrangements of Functions....Pages 333-352
A Class of I.M. Vinogradov’s Series and Its Applications in Harmonic Analysis....Pages 353-402
A Lower Bound for the de Bruijn-Newman Constant ?. II....Pages 403-418
On the Denseness of Weighted Incomplete Approximations....Pages 419-429
Asymptotics of Weighted Polynomials....Pages 431-451
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