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Lectures on Integral Transforms
 
N. I. Akhiezer
Lectures on Integral Transforms
Softcover ISBN:  978-0-8218-4524-0
Product Code:  MMONO/70
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4484-6
Product Code:  MMONO/70.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-4524-0
eBook: ISBN:  978-1-4704-4484-6
Product Code:  MMONO/70.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Add to cart
Lectures on Integral Transforms
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Lectures on Integral Transforms
N. I. Akhiezer
Softcover ISBN:  978-0-8218-4524-0
Product Code:  MMONO/70
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4484-6
Product Code:  MMONO/70.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-4524-0
eBook ISBN:  978-1-4704-4484-6
Product Code:  MMONO/70.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Add to cart
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 70; 1988; 108 pp
    MSC: Primary 44

    This book, which grew out of lectures given over the course of several years at Kharkov University for students in the Faculty of Mechanics and Mathematics, is devoted to classical integral transforms, principally the Fourier transform, and their applications. The author develops the general theory of the Fourier transform for the space \(L^1(E_n)\) of integrable functions of \(n\) variables. His proof of the inversion theorem is based on the general Bochner theorem on integral transforms, a theorem having other applications within the subject area of the book. The author also covers Fourier-Plancherel theory in \(L^2(E_n)\). In addition to the general theory of integral transforms, connections are established with other areas of mathematical analysis—such as the theory of harmonic and analytic functions, the theory of orthogonal polynomials, and the moment problem—as well as to mathematical physics.
  • Table of Contents
     
     
    • Chapters
    • Averaging operators and the Bochner theorem
    • The Fourier transform in $L^1$
    • The inversion theorem in $L^1$. The Poisson integral
    • Harmonic functions. The Dirichlet problem for a ball and a half-space
    • The Fourier transform in $L^2$
    • Hermite functions
    • Spherical functions
    • Positive definite functions
    • The Hankel transform
    • Orthogonal polynomials and the moment problem
    • The class $H^2$. The Paley-Wiener theorem
    • Boundary properties of functions analytic in the upper half-plane and the Hilbert transform
    • The Poisson summation formula and some of its applications
    • Applications of the Laplace and Fourier transforms to the solution of boundary value problems in mathematical physics
    • Fourier transforms of increasing functions. The Wiener-Hopf technique
  • Reviews
     
     

    • “This book is remarkable for its rigor, brevity, and systematic expression which, together with the problems proposed in each chapter, make it extremely useful for students, mathematicians, and physicists.”
      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Translations of Mathematical Monographs
Volume: 70; 1988; 108 pp
MSC: Primary 44

This book, which grew out of lectures given over the course of several years at Kharkov University for students in the Faculty of Mechanics and Mathematics, is devoted to classical integral transforms, principally the Fourier transform, and their applications. The author develops the general theory of the Fourier transform for the space \(L^1(E_n)\) of integrable functions of \(n\) variables. His proof of the inversion theorem is based on the general Bochner theorem on integral transforms, a theorem having other applications within the subject area of the book. The author also covers Fourier-Plancherel theory in \(L^2(E_n)\). In addition to the general theory of integral transforms, connections are established with other areas of mathematical analysis—such as the theory of harmonic and analytic functions, the theory of orthogonal polynomials, and the moment problem—as well as to mathematical physics.
  • Chapters
  • Averaging operators and the Bochner theorem
  • The Fourier transform in $L^1$
  • The inversion theorem in $L^1$. The Poisson integral
  • Harmonic functions. The Dirichlet problem for a ball and a half-space
  • The Fourier transform in $L^2$
  • Hermite functions
  • Spherical functions
  • Positive definite functions
  • The Hankel transform
  • Orthogonal polynomials and the moment problem
  • The class $H^2$. The Paley-Wiener theorem
  • Boundary properties of functions analytic in the upper half-plane and the Hilbert transform
  • The Poisson summation formula and some of its applications
  • Applications of the Laplace and Fourier transforms to the solution of boundary value problems in mathematical physics
  • Fourier transforms of increasing functions. The Wiener-Hopf technique

  • “This book is remarkable for its rigor, brevity, and systematic expression which, together with the problems proposed in each chapter, make it extremely useful for students, mathematicians, and physicists.”
    Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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