A01=Elias M. Stein
A01=Rami Shakarchi
Abelian group
Absolute value
Addition
Arithmetic progression
Author_Elias M. Stein
Author_Rami Shakarchi
Bernhard Riemann
Big O notation
Boundary value problem
Calculation
Category=PBKF
Cauchy sequence
Change of variables
Complex analysis
Complex number
Continuous function
Continuous function (set theory)
Convolution
Coprime integers
Corollary
Derivative
Differentiable function
Differential equation
Dimension
Dirichlet character
Dirichlet problem
Division by zero
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Euler's formula
Existential quantification
Exponential function
Fourier
Fourier analysis
Fourier inversion theorem
Fourier series
Fourier transform
Heat equation
Heat kernel
Hilbert space
Initial condition
Integer
Lebesgue integration
Lecture
Linear map
Logarithm
Mathematics
Natural number
Number theory
Order of integration (calculus)
Ordinary differential equation
Parametrization
Parseval's identity
Partial differential equation
Periodic function
Poisson kernel
Poisson summation formula
Polynomial
Quantity
Radon transform
Real number
Rectangle
Riemann integral
Scientific notation
Series (mathematics)
Summation
Theorem
Trigonometric functions
Trigonometric polynomial
Unit circle
Upper half-plane
Variable (mathematics)
Vector space
Wave equation
Product details
- ISBN 9780691113845
- Weight: 612g
- Dimensions: 152 x 235mm
- Publication Date: 06 Apr 2003
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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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. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis.
Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Elias M. Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph.D. in Mathematics from Princeton University in 2002.
