Best Books on Transform Theorems

“An Introduction to the Uncertainty Principle: Hardy’s Theorem on Lie Groups (Progress in Mathematics)” Book Review: This book gives a basic introduction to the uncertainty principle. It discusses Hardy’s theorem on Lie groups and covers different topics including interpolation, symbolic relations, and separation of symbols. It explains interpolation formulas for equal intervals, inverse interpolation using Lagrange’s formula, central difference formulas, curve fitting methods like the method of least square, curvilinear regression, and curve fitting by a sum of exponentials. The book also explores other related concepts and techniques.

“Fourier Series (Dover Books on Mathematics)” Book Review: This book offers a comprehensive exploration of the Fourier series, providing a detailed overview of its key concepts. It covers a range of topics, including trigonometric Fourier series, orthogonal systems, the summation and convergence of trigonometric Fourier series, double Fourier series, and the Fourier integral. Additionally, the book delves into trigonometric series with decreasing coefficients, operations on Fourier series, Bessel functions and Fourier-Bessel series, as well as the Eigenfunction method and its applications to mathematical physics. It is specifically designed for students, teachers, and professionals in various fields of science and technology, with a particular emphasis on computer engineering.

“Nonoscillation Theory of Functional Differential Equations with Applications” Book Review: This book offers a comprehensive overview of the non-oscillation theory of functional differential equations, along with its practical applications. It explores the application of differential equations to maximum principles, boundary value problems, and the stability of these equations. The book covers various topics, including scalar equations and systems of different types, equations with variable types of delays, and equations with variable deviations of the argument. Additionally, it delves into curve fitting, numerical solutions of ordinary differential equations, Fourier series, Fourier coefficients, Euler’s formulae in the interval (a, a + 2π), and Dirichlet’s conditions for the Fourier series expansion of a function. These topics, along with others, are discussed in detail throughout the book.