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About
Fredholm equation
(Definition)
A
Fredholm equation of the first kind
is an
integral equation
of the form
and a
Fredholm equation of the second kind
is an integral equation of the form
where
is a
compact operator
in some
function space
.
"Fredholm equation" is owned by
ncrom
.
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Cross-references:
function space
,
compact operator
,
integral equation
There is
1 reference
to this entry.
This is
version 2
of
Fredholm equation
, born on 2006-04-07, modified 2006-04-07.
Object id is
7805
, canonical name is
FredholmEquation
.
Accessed 1703 times total.
Classification:
AMS MSC
:
45B05
(Integral equations :: Fredholm integral equations)
Pending Errata and Addenda
None.
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![$\displaystyle \int_{a}^{b} K(x,y) f(y) dy = g(x), \quad \forall x \in [a,b], $](http://images.planetmath.org:8080/cache/objects/7805/l2h/img1.png "$\displaystyle \int_{a}^{b} K(x,y) f(y) dy = g(x), \quad \forall x \in [a,b], $")
![$\displaystyle f(x) - \lambda\int_{a}^{b} K(x,y)f(y)dy = g(x), \quad \forall x \in [a, b], $](http://images.planetmath.org:8080/cache/objects/7805/l2h/img2.png "$\displaystyle f(x) - \lambda\int_{a}^{b} K(x,y)f(y)dy = g(x), \quad \forall x \in [a, b], $")
![$\displaystyle Kf(x) = \int_{a}^{b} K(x,y)f(y)dy, \quad \forall x \in [a, b] $](http://images.planetmath.org:8080/cache/objects/7805/l2h/img3.png "$\displaystyle Kf(x) = \int_{a}^{b} K(x,y)f(y)dy, \quad \forall x \in [a, b] $")