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Convergence of polyharmonic splines on semi-regular grids Z x aZ^n  for a to 0

Institution: Springer
Region:
Description:

Let
p,n

N
with 2
p

n
+ 2
,
and let
I
a
be a polyharmonic spline of
order
p
on the grid
Z
×
a
Z
n
which satisfies the interpolating conditions
I
a
(
j,am
) =
d
j
(
am
) for
j

Z
,m

Z
n
where the functions
d
j
:
R
n

R
and the parameter
a>
0 are given. Let
B
s
(
R
n
) be the set of all integrable
functions
f
:
R
n

C
such that the integral
k
f
k
s
:=
Z
R
n
b
f
(
ξ
)
(1 +
|
ξ
|
s
)

is finite. The main result states that for given
σ

0 there exists a
constant
c>
0 such that whenever
d
j

B
2
p
(
R
n
)

C
(
R
n
)
,j

Z
,
satisfy
k
d
j
k
2
p

D
·
(1 +
|
j
|
σ
) for all
j

Z
there exists a polyspline
S
:
R
n
+1

C
of order
p
on strips such that
|
S
(
t,y
)

I
a
(
t,y
)
|≤
a
2
p

1
c
·
D
·
(1 +
|
t
|
σ
)
for all
y

R
n
,t

R
and all 0

1.

Related: http://dx.doi.org/10.1007/s11075-007-9099-x
Suggested citation:

. () Convergence of polyharmonic splines on semi-regular grids Z x aZ^n  for a to 0 [Online]. Available from: http://publichealthwell.ie/node/775175 [Accessed: 16th July 2019].

  

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