Asymptotics of resolvent iterates for abstract potentials

Shmuel Kantorovitz

doi:10.1007/s00233-003-0022-z

Asymptotics of resolvent iterates for abstract potentials

Shmuel Kantorovitz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let A be an abstract potential, that is, an operator whose resolvent R(·) exists and satisfies the condition ∥(ℛλ - a)R(λ)∥ ≤ M in a halfplane Π_a: = {λ ∈ ℂ; ℛλ > a}. It is shown that the resolvent iterates satisfy in Π_a the estimates ∥[(ℛλ - a)R(λ)] ⁿ∥ < Men for all n ∈ ℕ.

Original language	English
Pages (from-to)	491-494
Number of pages	4
Journal	Semigroup Forum
Volume	68
Issue number	3
DOIs	https://doi.org/10.1007/s00233-003-0022-z
State	Published - May 2004

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title = "Asymptotics of resolvent iterates for abstract potentials",

abstract = "Let A be an abstract potential, that is, an operator whose resolvent R(·) exists and satisfies the condition ∥(ℛλ - a)R(λ)∥ ≤ M in a halfplane Πa: = {λ ∈ ℂ; ℛλ > a}. It is shown that the resolvent iterates satisfy in Πa the estimates ∥[(ℛλ - a)R(λ)] n∥ < Men for all n ∈ ℕ.",

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AB - Let A be an abstract potential, that is, an operator whose resolvent R(·) exists and satisfies the condition ∥(ℛλ - a)R(λ)∥ ≤ M in a halfplane Πa: = {λ ∈ ℂ; ℛλ > a}. It is shown that the resolvent iterates satisfy in Πa the estimates ∥[(ℛλ - a)R(λ)] n∥ < Men for all n ∈ ℕ.

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Asymptotics of resolvent iterates for abstract potentials

Abstract

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