Elias M Stein

Elias M Stein - Fourier analysis

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• This first volume
• A three-part introduction to the subject
• Is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis
• It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions
• The first part implements this idea in terms of notions of convergence and summability of Fourier series
• While highlighting applications such as the isoperimetric inequality and equidistribution
• The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform
• A clear introduction to the subject serves to avoid technical difficulties
• The book closes with Fourier theory for finite abelian groups
• Which is applied to prime numbers in arithmetic progression

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