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In [[mathematics]], the '''Bessel potential''' is a [[potential theory|potential]] (named after [[Friedrich Wilhelm Bessel]]) similar to the '''[[Riesz potential]]''' but with better decay properties at infinity.


If ''s'' is a complex number with positive real part then the Bessel potential of order ''s'' is the operator
:<math>(I-\Delta)^{-s/2}</math>
where Δ is the [[Laplace operator]] and the [[fractional calculus|fractional power]] is defined using Fourier transforms.


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==See also==
* [[Riesz potential]]
* [[Fractional integration]]
* [[Sobolev space]]
* [[Fractional Schrödinger equation]]
 
==References==
*{{eom|id=B/b110420|title=Bessel potential operator|first=R. |last=Duduchava}}
*{{Citation | last1=Grafakos | first1=Loukas | title=Modern Fourier analysis | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | series=Graduate Texts in Mathematics | isbn=978-0-387-09433-5 | doi=10.1007/978-0-387-09434-2 | mr=2463316 | year=2009 | volume=250}}
*{{eom|id=B/b120170|title=Bessel potential space|first=L.I. |last= Hedberg}}
*{{eom|id=B/b015870|first=E.D.|last= Solomentsev}}
* {{citation |first=Elias |last=Stein |authorlink=Elias Stein |title=Singular integrals and differentiability properties of functions |publisher=[[Princeton University Press]] |location=Princeton, NJ |year=1970 |isbn=0-691-08079-8}}
 
[[Category:Fractional calculus]]
[[Category:Partial differential equations]]
[[Category:Potential theory]]
[[Category:Singular integrals]]

Revision as of 23:32, 10 December 2013

In mathematics, the Bessel potential is a potential (named after Friedrich Wilhelm Bessel) similar to the Riesz potential but with better decay properties at infinity.

If s is a complex number with positive real part then the Bessel potential of order s is the operator

(IΔ)s/2

where Δ is the Laplace operator and the fractional power is defined using Fourier transforms.

See also

References

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