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Integral Representations and Isomorphism of Isotropy Classes

  • S. M. Nikol’skii
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 205)

Abstract

The Fourier-transform of the function (1 + |x|2)r/2, for sufficiently large r > 0, may be obtained effectively, since it is a function of |x|, and the well-known formula1 $$\matrix{\overline{(1+\mid x\mid^2)^{-r/2}}={1\over (2\pi)^{n/2}}\int {e^{iu\xi}d\xi\over (1+\mid \xi \mid^2)^{r/2}}\cr ={1\over{\mid u\mid^{{n-r}\over 2}}}{\mathop\int\limits_0^\infty}{\varrho^{n/2}\over (1+\varrho^2)^{r/2}}I_{{n-2}\over 2}(\mid u\mid\varrho)d\varrho,}$$ where Iμ is the Bessel Function of order μ, is applicable to it.

Keywords

Integral Representation Entire Function Regular Function Trigonometric Polynomial Exponential Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • S. M. Nikol’skii
    • 1
  1. 1.Sergei Mihailovič Nikol’skii Steklov MathematicalInstitute Academy of SciencesMoscowUSA

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