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Resolvent Operator


The resolvent operator of a closed operator A on a complex Banach space X at a point lambda in its resolvent set is the bounded operator

 R(lambda,A)=(lambdaI-A)^(-1),

where I is the identity operator. The family R(lambda,A) for lambda in the resolvent set is called the resolvent of A. Bounds on resolvent operators are central to the study of operator spectrum and semigroup stability.


See also

Gearhart-Prüss-Huang Theorem, Operator Spectrum, Resolvent Set, Semigroup Stability

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References

Conway, J. B. A Course in Functional Analysis. New York: Springer-Verlag, 1990.

Cite this as:

Weisstein, Eric W. "Resolvent Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ResolventOperator.html

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