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    Rights statement: Copyright © 2017 by Walter de Gruyter GmbH

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Operational calculus and integral transforms for groups with finite propagation speed

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Operational calculus and integral transforms for groups with finite propagation speed. / Blower, Gordon; Doust, Ian.
In: Advances in Pure and Applied Mathematics, Vol. 8, No. 4, 01.10.2017, p. 265-283.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Blower, G & Doust, I 2017, 'Operational calculus and integral transforms for groups with finite propagation speed', Advances in Pure and Applied Mathematics, vol. 8, no. 4, pp. 265-283. https://doi.org/10.1515/apam-2015-0049

APA

Blower, G., & Doust, I. (2017). Operational calculus and integral transforms for groups with finite propagation speed. Advances in Pure and Applied Mathematics, 8(4), 265-283. https://doi.org/10.1515/apam-2015-0049

Vancouver

Blower G, Doust I. Operational calculus and integral transforms for groups with finite propagation speed. Advances in Pure and Applied Mathematics. 2017 Oct 1;8(4):265-283. Epub 2017 May 25. doi: 10.1515/apam-2015-0049

Author

Blower, Gordon ; Doust, Ian. / Operational calculus and integral transforms for groups with finite propagation speed. In: Advances in Pure and Applied Mathematics. 2017 ; Vol. 8, No. 4. pp. 265-283.

Bibtex

@article{5ca3a344610c4424bde9b9db3ae4d74f,
title = "Operational calculus and integral transforms for groups with finite propagation speed",
abstract = "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. ",
keywords = "Operator groups, hypergroups, multipliers",
author = "Gordon Blower and Ian Doust",
note = "Copyright {\textcopyright} 2017 by Walter de Gruyter GmbH",
year = "2017",
month = oct,
day = "1",
doi = "10.1515/apam-2015-0049",
language = "English",
volume = "8",
pages = "265--283",
journal = "Advances in Pure and Applied Mathematics",
issn = "1867-1152",
publisher = "De Gruyter",
number = "4",

}

RIS

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 -