Additional Properties of Distributions

Ram P. Kanwal
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Ram P. Kanwal: The Pennsylvania State University, Department of Mathematics

Chapter Chapter 3 in Generalized Functions, 2004, pp 49-70 from Springer

Abstract: 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 1 $$ \delta \left[ {f\left( x \right)} \right] = \sum\limits_{m = 1}^n {\frac{{\delta \left( {x - x_m } \right)}} {{\left| {f'\left( {x_m } \right)} \right|}}} , $$ Where x m runs through the simple zeros of f (x).

Keywords: Fourier Series; Delta Function; Additional Property; Convergent Sequence; Simple Zero (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8174-6_3

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DOI: 10.1007/978-0-8176-8174-6_3

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