P. R. Halmos and V. S. Sunder. Bomded Itegral Operators o L 2 Spaces. Springer-Verlag, New York, 1978.  Home/Search   Document Not in Database   Summary   Related Articles

....way to write this is to show its action on a function f, K f) x) k(x, y) f(y) dy. 8) The above form of integral operator called a kernel operator , and k is called the kernel. The kernel k is essentially an extension of the concept of a matrix to an infinite dimensional function space [13]. It is easy to verify that K is a linear operator over an appropriate domain X, such as ( 0, 1] Indeed, for any f, g ff ( 0, 1] we have [K(f g) x) k(x,y) f g] y)dy : k(x, y) If(y) g(y) dy : k(x, y) f(y) dy k(x, y) g(y) dy : Kf) x) Kg) x) Since this holds for all x E [0, ....

P. R. Halmos and V. S. Sunder. Bomded Itegral Operators o L 2 Spaces. Springer-Verlag, New York, 1978.

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