Harmonic Functions
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Home > Art, Film & Photography > Harmonic Functions: Laplace's Equation, Harmonic Function, Cauchy-Riemann Equations, Laplace Operator, Hilbert Transform, Poisson Kernel
Harmonic Functions: Laplace's Equation, Harmonic Function, Cauchy-Riemann Equations, Laplace Operator, Hilbert Transform, Poisson Kernel

Harmonic Functions: Laplace's Equation, Harmonic Function, Cauchy-Riemann Equations, Laplace Operator, Hilbert Transform, Poisson Kernel


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 23. Chapters: Laplace's equation, Harmonic function, Cauchy-Riemann equations, Laplace operator, Hilbert transform, Poisson kernel, Riesz transform, Harnack's inequality, Newtonian potential, Harmonic conjugate, Harmonic coordinates, Maximum principle, Weyl's lemma, Kelvin transform, Dirichlet's principle, Schwarz reflection principle, Harnack's principle, Pluriharmonic function, Weakly harmonic function. Excerpt: In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u(t), and produces a function, H(u)(t), with the same domain. The Hilbert transform is named after David Hilbert, who first introduced the operator in order to solve a special case of the Riemann-Hilbert problem for holomorphic functions. It is a basic tool in Fourier analysis, and provides a concrete means for realizing the harmonic conjugate of a given function or Fourier series. Furthermore, in harmonic analysis, it is an example of a singular integral operator, and of a Fourier multiplier. The Hilbert transform is also important in the field of signal processing where it is used to derive the analytic representation of a signal u(t). The Hilbert transform was originally defined for periodic functions, or equivalently for functions on the circle, in which case it is given by convolution with the Hilbert kernel. More commonly, however, the Hilbert transform refers to a convolution with the Cauchy kernel, for functions defined on the real line R (the boundary of the upper half-plane). The Hilbert transform is closely related to the Paley-Wiener theorem, another result relating holomorphic functions in the upper half-plane and Fourier transforms of functions on the real line. The Hilbert transform, in red, of a square wave, in blue The Hilbert transform can be thought of as the convolution of u(t) with the functio...


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Product Details
  • ISBN-13: 9781155671208
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Weight: 64 gr
  • ISBN-10: 1155671201
  • Publisher Date: 07 Jul 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Laplace's Equation, Harmonic Function, Cauchy-Riemann Equations, Laplace Operator, Hilbert Transform, Poisson Kernel
  • Width: 189 mm


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