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References (38)
-
R. Coifman, G. Weiss (1977)
Transference methods in analysis -
Paul Cherno (1973)
Essential self-adjointness of powers of generators of hyperbolic equations -
I. Sneddon (1972)
The use of integral transforms -
G. Blower (2000)
Maximal functions and transference for groups of operatorsProceedings of the Edinburgh Mathematical Society, 43
-
(1987)
Ste čkin’s theorem -
E. Berkson, T. Gillespie (1987)
Stečkin's Theorem, transference, and spectral decompositionsJournal of Functional Analysis, 70
-
J. Goldstein (1985)
Semigroups of Linear Operators and Applications -
Edmund Whittaker, G. Watson (2021)
A Course of Modern Analysis -
Wolfgang Hackbusch (2014)
Ordinary Differential Equations -
Michael Taylor (2009)
Functions of the Laplace Operator on Manifolds with Lower Ricci and Injectivity BoundsCommunications in Partial Differential Equations, 34
-
L. Debnath (2012)
Tables of Integral Transforms -
W. Bloom, H. Heyer (1994)
Harmonic Analysis of Probability Measures on Hypergroups -
M. Voit (1988)
Positive characters on commutative hypergroups and some applicationsMathematische Zeitschrift, 198
-
H. Zeuner (1989)
One-dimensional hypergroupsAdvances in Mathematics, 76
-
N. Bhatia (1964)
Lectures on ordinary differential equations -
R. Strichartz (1983)
Analysis of the Laplacian on the Complete Riemannian ManifoldJournal of Functional Analysis, 52
-
F. Mehler (1881)
Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der ElektricitätsvertheilungMathematische Annalen, 18
-
G. Blower (1996)
Multipliers for semigroupsProceedings of the Edinburgh Mathematical Society, 39
-
M. Cowling, I. Doust, Alan Micintosh, A. Yagi (1996)
Banach space operators with a bounded H∞ functional calculusJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 60
-
C. Travis, G. Webb (1978)
Cosine families and abstract nonlinear second order differential equationsActa Mathematica Academiae Scientiarum Hungarica, 32
-
(2001)
Isoperimetric Inequalities -
T. MacRobert (1955)
Higher Transcendental FunctionsNature, 175
-
C. Hammer (1953)
Higher transcendental functions, Volume I: by Harry Bateman (compiled by the staff of the Bateman Manuscript Project). 302 pages, 16 × 24 cm. New York, McGraw-Hill Book Co., Inc., 1953. Price, $6.50Journal of The Franklin Institute-engineering and Applied Mathematics, 256
-
M. Haase (2008)
A transference principle for general groups and functional calculus on UMD spacesMathematische Annalen, 345
-
K. Boyadzhiev, R. Delaubenfels (1994)
Spectral theorem for unbounded strongly continuous groups on a Hilbert space, 120
-
Houcine Chébli (1978)
Théorème de Paley-Wiener associé à un opérateur différentiel singulier sur $(0,\infty)$ -
P. Lax, R. Phillips (1982)
The asymptotic distribution of lattice points in Euclidean and non-Euclidean spacesJournal of Functional Analysis, 46
-
P. Hartman (1965)
Ordinary Differential EquationsJournal of the American Statistical Association, 60
-
G. Gigante (2001)
Transference for hypergroupsCollectanea Mathematica, 52
-
M. Uiterdijk (2000)
A functional calculus for analytic generators ofC0-groupsIntegral Equations and Operator Theory, 36
-
(1982)
Finite propagation s peed -
J. Cheeger, M. Gromov, Michael Taylor (1982)
Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifoldsJournal of Differential Geometry, 17
-
R. Jewett (1975)
Spaces with an abstract convolution of measuresAdvances in Mathematics, 18
-
E. Stein (1970)
Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. -
I. Chavel (2006)
Riemannian Geometry: Isoperimetric Inequalities (Constant Curvature) -
M. Taylor (1989)
Lp-estimates on functions of the Laplace operatorDuke Mathematical Journal, 58
-
Houcine Chébli (1974)
Sur un théorème de Paley-Wiener associéà la décomposition spectrale d'un opérateur de Sturm-Liouville sur ]0, ∞[Journal of Functional Analysis, 17
-
I. Chavel (1984)
Eigenvalues in Riemannian geometry
- Publisher
- de Gruyter
- Copyright
- © 2017 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 1869-6090
- eISSN
- 1869-6090
- DOI
- 10.1515/apam-2015-0049
- Publisher site
- See Article on Publisher Site
Abstract
AbstractLet A be the generator of a strongly continuous cosine family (cos(tA))t∈ℝ{(\cos(tA))_{t\in\mathbb{R}}}on a complex Banach space E. The paper develops an operational calculus for integral transforms and functions of A using the generalized harmonic analysis associated to certain hypergroups. It is shown that characters of hypergroups which have Laplace representations give rise to bounded operators on E. Examples include the Mellin transform and the Mehler–Fock transform. The paper usesfunctional calculus for the cosine family cos(tΔ){\cos(t\sqrt{\Delta})}which isassociated 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.
Journal
Advances in Pure and Applied Mathematics – de Gruyter
Published: Oct 1, 2017