Topics in Classical and Modern Analysis: In Memory of Yingkang Hu

Description

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume. Front Matter ....Pages i-xxiii Front Matter ....Pages 1-18 On Some Properties of Moduli of Smoothness with Jacobi Weights (Kirill A. Kopotun, Dany Leviatan, Igor A. Shevchuk)....Pages 19-31 Front Matter ....Pages 33-33 Special Difference Operators and the Constants in the Classical Jackson-Type Theorems (Alexander G. Babenko, Yuriy V. Kryakin)....Pages 35-46 Comparison Theorems for Completely and Multiply Monotone Functions and Their Applications (Vladyslav Babenko, Yuliya Babenko, Oleg Kovalenko)....Pages 47-64 Concerning Exponential Bases on Multi-Rectangles of \(\boldsymbol {\mathbb {R}^d}\) (Laura De Carli)....Pages 65-85 Hankel Transforms of General Monotone Functions (Alberto Debernardi)....Pages 87-104 Univalence of a Certain Quartic Function (Jimmy Dillies)....Pages 105-108 Finding, Stabilizing, and Verifying Cycles of Nonlinear Dynamical Systems (Dmitriy Dmitrishin, Ionut E. Iacob, Ivan Skrinnik, Alex Stokolos)....Pages 109-125 Finding Orbits of Functions Using Suffridge Polynomials (Dmitriy Dmitrishin, Paul Hagelstein, Alex Stokolos)....Pages 127-133 The Sharp Remez-Type Inequality for Even Trigonometric Polynomials on the Period (Tamás Erdélyi)....Pages 135-145 The Lebesgue Constants of Fourier Partial Sums (Michael I. Ganzburg, Elijah Liflyand)....Pages 147-158 Liouville–Weyl Derivatives of Double Trigonometric Series (Ainur Jumabayeva, Boris Simonov)....Pages 159-182 Inequalities in Approximation Theory Involving Fractional Smoothness in Lp, 0