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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Operational calculus and integral transforms for groups with finite propagation speed
AU - Blower, Gordon
AU - Doust, Ian
N1 - Copyright © 2017 by Walter de Gruyter GmbH
PY - 2017/10/1
Y1 - 2017/10/1
N2 - Let A be the generator of a strongly continuous cosine family (cos tA)) on a complex Banach space E. The paper develops an operational calculus for integral transforms and functions of A using the generalized harmonic analysis assocaited to certain hypergroups. It is shown that characters of hypergroups which have laplace representation give rise to bounded operators on E. Examples include the Mellin trasnform and the Mehler--Fock transform. The paper uses functional caclulus for the cosine family that is associated with waves that travel at unit speed. The main results include an operational calculus theorem for Sturm--Liouville hypergroups with Laplace representation as well as analogues to the Kunze--Stein phenomenon in the hypergroup convolution setting.
AB - Let A be the generator of a strongly continuous cosine family (cos tA)) on a complex Banach space E. The paper develops an operational calculus for integral transforms and functions of A using the generalized harmonic analysis assocaited to certain hypergroups. It is shown that characters of hypergroups which have laplace representation give rise to bounded operators on E. Examples include the Mellin trasnform and the Mehler--Fock transform. The paper uses functional caclulus for the cosine family that is associated with waves that travel at unit speed. The main results include an operational calculus theorem for Sturm--Liouville hypergroups with Laplace representation as well as analogues to the Kunze--Stein phenomenon in the hypergroup convolution setting.
KW - Operator groups
KW - hypergroups
KW - multipliers
U2 - 10.1515/apam-2015-0049
DO - 10.1515/apam-2015-0049
M3 - Journal article
VL - 8
SP - 265
EP - 283
JO - Advances in Pure and Applied Mathematics
JF - Advances in Pure and Applied Mathematics
SN - 1867-1152
IS - 4
ER -