N-Tupling Transformations and Invariant Definite Integrals
Functions on the real number line of the type ψ ( x ) = c + x - b x - μ , with b > 0 , have the interesting property that for any continuous, absolutely integrable function F on R , the graph of F ( ψ ( x ) ) is a “doubling” of the graph of F ( x ) , while the integral over R remains invariant, ∫...
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| Veröffentlicht in: | International journal of applied and computational mathematics 2015-12, Vol.1 (4), p.527-541 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Functions on the real number line of the type
ψ
(
x
)
=
c
+
x
-
b
x
-
μ
,
with
b
>
0
, have the interesting property that for any continuous, absolutely integrable function
F
on
R
, the graph of
F
(
ψ
(
x
)
)
is a “doubling” of the graph of
F
(
x
)
, while the integral over
R
remains invariant,
∫
-
∞
∞
F
(
ψ
(
x
)
)
d
x
=
∫
-
∞
∞
F
(
x
)
d
x
. In this paper, we discover new families of
n
-to-1 mappings on
R
that have the same invariance property. |
|---|---|
| ISSN: | 2349-5103 2199-5796 |
| DOI: | 10.1007/s40819-015-0025-y |