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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.

Difference equations. --- Functional equations. --- Harmonic analysis. --- Functional analysis. --- Functions of complex variables. --- Functions of real variables. --- Difference and Functional Equations. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Functions of a Complex Variable. --- Real Functions. --- Trigonometric sums. --- Sums, Trigonometric --- Exponential sums --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Real variables --- Functions of complex variables