On an integral of fractional power operators

Nick Dungey. "On an integral of fractional power operators." Colloquium Mathematicae 117.2 (2009): 157-164. <http://eudml.org/doc/286393>.

@article{NickDungey2009,
abstract = {For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator $Ṽ = ∫_\{0\}^\{∞\} dα V^\{α\}$. We show, for example, that Ṽ is sectorial, and asymptotically of type 0. If V has single-point spectrum 0, then Ṽ is of type 0 with a single-point spectrum, and the operator I-Ṽ satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.},
author = {Nick Dungey},
journal = {Colloquium Mathematicae},
keywords = {fractional power; functional calculus; sectorial operator; Ritt resolvent condition; Volterra operator},
language = {eng},
number = {2},
pages = {157-164},
title = {On an integral of fractional power operators},
url = {http://eudml.org/doc/286393},
volume = {117},
year = {2009},
}

TY - JOUR
AU - Nick Dungey
TI - On an integral of fractional power operators
JO - Colloquium Mathematicae
PY - 2009
VL - 117
IS - 2
SP - 157
EP - 164
AB - For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator $Ṽ = ∫_{0}^{∞} dα V^{α}$. We show, for example, that Ṽ is sectorial, and asymptotically of type 0. If V has single-point spectrum 0, then Ṽ is of type 0 with a single-point spectrum, and the operator I-Ṽ satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.
LA - eng
KW - fractional power; functional calculus; sectorial operator; Ritt resolvent condition; Volterra operator
UR - http://eudml.org/doc/286393
ER -