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- Shift_theorem abstract "In mathematics, the (exponential) shift theorem is a theorem about polynomial differential operators (D-operators) and exponential functions. It permits one to eliminate, in certain cases, the exponential from under the D-operators.The theorem states that, if P(D) is a polynomial D-operator, then, for any sufficiently differentiable function y,To prove the result, proceed by induction. Note that only the special caseneeds to be proved, since the general result then follows by linearity of D-operators.The result is clearly true for n = 1 since Now suppose the result true for n = k, that is,Then,This completes the proof.The shift theorem applied equally well to inverse operators: There is a similar version of the shift theorem for Laplace transforms :".
- Shift_theorem wikiPageID "13795874".
- Shift_theorem wikiPageRevisionID "461762315".
- Shift_theorem hasPhotoCollection Shift_theorem.
- Shift_theorem subject Category:Differential_operators.
- Shift_theorem subject Category:Multivariable_calculus.
- Shift_theorem subject Category:Theorems_in_analysis.
- Shift_theorem type Abstraction100002137.
- Shift_theorem type Communication100033020.
- Shift_theorem type DifferentialOperators.
- Shift_theorem type Function113783816.
- Shift_theorem type MathematicalRelation113783581.
- Shift_theorem type Message106598915.
- Shift_theorem type Operator113786413.
- Shift_theorem type Proposition106750804.
- Shift_theorem type Relation100031921.
- Shift_theorem type Statement106722453.
- Shift_theorem type Theorem106752293.
- Shift_theorem type TheoremsInAnalysis.
- Shift_theorem comment "In mathematics, the (exponential) shift theorem is a theorem about polynomial differential operators (D-operators) and exponential functions. It permits one to eliminate, in certain cases, the exponential from under the D-operators.The theorem states that, if P(D) is a polynomial D-operator, then, for any sufficiently differentiable function y,To prove the result, proceed by induction.".
- Shift_theorem label "Shift theorem".
- Shift_theorem sameAs m.03cjhyt.
- Shift_theorem sameAs Q7496252.
- Shift_theorem sameAs Q7496252.
- Shift_theorem sameAs Shift_theorem.
- Shift_theorem wasDerivedFrom Shift_theorem?oldid=461762315.
- Shift_theorem isPrimaryTopicOf Shift_theorem.