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Full Description
This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.
Contents
On a category of cotangent sums related to the Nyman-Beurling criterion for the Riemann Hypothesis.- Recent Progress in the study of polynomials with constrained coefficients.- Classes of Nonnegative Sine .- Inequalities for weighted trigonometric sums.- Norm Inequalities for Generalized Laplace Transforms.- On Marcinkiewicz-Zygmund Inequalities at Hermite Zeros and their Airy Function Cousins.- The maximum of cotangent sums related to the Nyman-Beurling criterion for the Riemann Hypothesis.- Double-sided Taylor's approximations and their applications in theory of trigonometric inequalities.- Double-sided Taylor's approximations and their applications in theory of trigonometric inequalities.- The second moment of the first derivative of Hardy's Z-function.- Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas.- On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function.- A remark on sets with small Wiener norm.- Order estimates of best orthogonal trigonometric approximations of classes of infinitely differentiable functions.- Equivalent Conditions of a Reverse Hilbert-Type Integral Inequality with the Kernel of Hyperbolic Cotangent Function Related to the Riemann zeta Function
