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Additional Properties of Distributions

  • Ram P. Kanwal

Abstract

Some algebraic operations on the delta function were studied in the last chapter. In subsequent chapters we shall be required to transform this function to certain curvilinear coordinates. For this purpose we devote an entire section to this topic. Let us first study the meaning of the function δ[f(x)] and prove the result
$$ \delta \left[ {f\left( x \right)} \right] = \sum\limits_{m = 1}^n {\frac{{\delta \left( {x - x_m } \right)}} {{\left| {f'\left( {x_m } \right)} \right|}}} , $$
(1)
Where x m runs through the simple zeros of f (x).

Keywords

Fourier Series Delta Function Additional Property Convergent Sequence Simple Zero 
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 Science+Business Media New York 2004

Authors and Affiliations

  • Ram P. Kanwal
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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