From Wikipedia, the free encyclopedia

does not represent antidifferentiation on L^2(0,1)

An L^2 function doesnt even need to have an antiderivative and even even if almost-everywhere-antiderivatives are allowed, they don't need to equal the Volterra integral (not even almost everywhere). Example for both: f(x)=0, for x<1/2, f(x)=1, for x>1/2. I will adjust the article unless someone has objections. Ninjamin ( talk) 17:35, 16 May 2019 (UTC) reply

More properties

Some additional properties of the Volterra operator:

  • For each , is Hölder continuous with exponent . Stated and proved in the StackExchange answer linked in the article.
  • Using Fubini's theorem one can compute repeated applications of as .

Because I don't have a source (other than lecture notes) on the latter statement, I didn't want to add them to the article. Columbus240 ( talk) 13:29, 12 January 2022 (UTC) reply

From Wikipedia, the free encyclopedia

does not represent antidifferentiation on L^2(0,1)

An L^2 function doesnt even need to have an antiderivative and even even if almost-everywhere-antiderivatives are allowed, they don't need to equal the Volterra integral (not even almost everywhere). Example for both: f(x)=0, for x<1/2, f(x)=1, for x>1/2. I will adjust the article unless someone has objections. Ninjamin ( talk) 17:35, 16 May 2019 (UTC) reply

More properties

Some additional properties of the Volterra operator:

  • For each , is Hölder continuous with exponent . Stated and proved in the StackExchange answer linked in the article.
  • Using Fubini's theorem one can compute repeated applications of as .

Because I don't have a source (other than lecture notes) on the latter statement, I didn't want to add them to the article. Columbus240 ( talk) 13:29, 12 January 2022 (UTC) reply


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