and the associated Hilbert-Schmidt integral operator is the operator K : L²(Ω; C) → L²(Ω; C) given by

$(K\; u)\; (x)\; =\; int\_\{Omega\}\; k(x,\; y)\; u(y)\; ,\; dy.$

Hilbert-Schmidt integral operators are both continuous (and hence bounded) and compact.

See also

• Hilbert-Schmidt operator

References

• Renardy, Michael and Rogers, Robert C. (2004). An introduction to partial differential equations. Second edition, New York: Springer-Verlag. (Sections 7.1 and 7.5)