A Functional Calculus for (α, α +1 )− type R Operators

@inproceedings{Oleche2010AFC,
  title={A Functional Calculus for (α, α +1 )− type R Operators},
  author={Paul Odhiambo Oleche and John O. Agure},
  year={2010}
}
A closed densely defined operator H, on a Banach space X , whose spectrum is contained in R and satisfies ∥∥(z − H)−1∥∥ ≤ c 〈z〉 | z| ∀ z ∈ R with 〈z〉 := √ |z| + 1 (1) for some α , β ≥ 0; c > 0, is said to be of (α, β) − type R (notation introduced in [10]). For (α, α + 1)− type R operators we constructed an A-functional calculus in a more general Banach space setting (where A is the algebra of smooth functions on R that decay like ( √ 1 + x2)β as |x| → ∞, for some β < 0. This algebra is fully… CONTINUE READING

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