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can we generalize the cauchy principal value and hadamard's finite part for multiple integrals $ n>1 $

iI have observed and studiedseen in wikipedia, that how the Cauchy's pricnipal value and Hadamard's finite part work in ONE dimension one

myMy question is whey wewhen can we (or if negative answer why can not ) generalize the Hadamard's finite part and Cauchy's principal value to include integration over several variables: surface integral volume integral and so on ?

can we generalize cauchy principal value and hadamard's finite part for multiple integrals $ n>1 $

i have observed and studied in wikipedia, how the Cauchy's pricnipal value and Hadamard's finite part work in ONE dimension

my question is whey we can (or if negative answer why can not ) generalize the Hadamard's finite part and Cauchy's principal value to include integration over several variables: surface integral volume integral and so on ?

can we generalize the cauchy principal value and hadamard's finite part for multiple integrals $ n>1 $

I have seen in wikipedia, that how the Cauchy's pricnipal value and Hadamard's finite part work in dimension one

My question is when can we (or if negative answer why can not ) generalize the Hadamard's finite part and Cauchy's principal value to include integration over several variables: surface integral volume integral and so on ?

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can we generalize cauchy principal value and hadamard's finite part for multiple integrals $ n>1 $

i have observed and studied in wikipedia, how the Cauchy's pricnipal value and Hadamard's finite part work in ONE dimension

my question is whey we can (or if negative answer why can not ) generalize the Hadamard's finite part and Cauchy's principal value to include integration over several variables: surface integral volume integral and so on ?