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Home > Art, Film & Photography > Singular Integrals: Hilbert Transform, Singular Integral, Riesz Transform, Newtonian Potential, Riesz Potential, Bessel Potential
Singular Integrals: Hilbert Transform, Singular Integral, Riesz Transform, Newtonian Potential, Riesz Potential, Bessel Potential

Singular Integrals: Hilbert Transform, Singular Integral, Riesz Transform, Newtonian Potential, Riesz Potential, Bessel Potential


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About the Book

Chapters: Hilbert Transform, Singular Integral, Riesz Transform, Newtonian Potential, Riesz Potential, Bessel Potential. Source: Wikipedia. Pages: 41. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. 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 RiemannHilbert problem for holomorphic functions. It is a basic tool in Fourier analysis, and provides a concrete means for realizing the 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 PaleyWiener 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 function h(t) = 1/( t). Because h(t) is not integrable the integrals defining the convolution do not converge. Instead, the Hilbert transform is defined using the Cauchy principal value (denoted h...More: http: //booksllc.net/?id=57402


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Product Details
  • ISBN-13: 9781156300039
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 42
  • Spine Width: 3 mm
  • Weight: 77 gr
  • ISBN-10: 1156300037
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Hilbert Transform, Singular Integral, Riesz Transform, Newtonian Potential, Riesz Potential, Bessel Potential
  • Width: 229 mm


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