MHB Converging to Delta(y-b): Solving the Limit of f_x((y-b)/a) as a Approaches 0

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SUMMARY

The limit lim 1/|a| f_x((y-b)/a) as a approaches 0 converges to the Dirac delta function delta(y-b). This conclusion is established through the properties of distributions, specifically in the context of generalized functions. The discussion emphasizes the need for clarity in defining terms such as "delta(y-b)" and "f_x" to ensure accurate interpretation of the limit.

PREREQUISITES
  • Understanding of the Dirac delta function
  • Familiarity with limits in calculus
  • Knowledge of distribution theory
  • Basic concepts of generalized functions
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  • Study the properties of the Dirac delta function in detail
  • Explore distribution theory and its applications in mathematical analysis
  • Learn about limits involving generalized functions
  • Investigate the role of f_x in the context of distributions
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Mathematicians, physicists, and students studying advanced calculus or distribution theory who seek to understand the convergence of limits involving the Dirac delta function.

luppin
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Show the following limit will converge to delta(y-b),

lim 1/|a| f_x((y-b)/a)=delta(y-b)
a-->0
 
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How are you defining "delta(y- b)"?
 
And what is [math]f_x[/math]?

-Dan
 
luppin said:
Show the following limit will converge to delta(y-b),

lim 1/|a| f_x((y-b)/a)=delta(y-b)
a-->0

Problem definition is not clear.
 

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