In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator T ( f ) ( x ) = ∫ K ( x , y ) f ( y ) d y , {\displaystyle T(f)(x)=\int K(x,y)f(y)\,dy,} whose kernel function K : R n × R n → R {\displaystyle K:\mathbb {R} ^{n}\times \mathbb {R} ^{n}\to \mathbb {R} } is singular along the diagonal x = y {\displaystyle x=y} .
In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator T ( f ) ( x ) = ∫ K ( x , y ) f ( y ) d y , {\displaystyle T(f)(x)=\int K(x,y)f(y)\,dy,} whose kernel function K : R n × R n → R {\displaystyle K:\mathbb {R} ^{n}\times \mathbb {R} ^{n}\to \mathbb {R} } is singular along the diagonal x = y {\displaystyle x=y} .
Source: Wikipedia "Singular integral" · CC BY-SA 4.0
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