Abstract
Let A be the generator of a strongly continuous cosine family
Funding statement: This research was partially supported by a Scheme 2 Grant from the London Mathematical Society.
Acknowledgements
Gordon Blower thanks the University of New South Wales for hospitality.
References
[1] E. Berkson and T. A. Gillespie, Stečkin’s theorem, transference and spectral decompositions, J. Funct. Anal. 70 (1987), 140–170. 10.1016/0022-1236(87)90128-5Search in Google Scholar
[2] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, De Gruyter, Berlin, 1994. 10.1515/9783110877595Search in Google Scholar
[3] G. Blower, Multipliers for semigroups, Proc. Edin. Math. Soc. (2) 39 (1996), 241–252. 10.1017/S0013091500022975Search in Google Scholar
[4] K. Boyadzhiev and R. deLaubenfels, Spectral theorem for unbounded strongly continuous groups on a Hilbert space, Proc. Amer. Math. Soc. 120 (1994), 127–136. 10.1090/S0002-9939-1994-1186983-0Search in Google Scholar
[5] I. Chavel, Riemannian Geometry – A Modern Introduction, Cambridge Tracts in Math. 108, Cambridge University Press, Cambridge, 1993. Search in Google Scholar
[6] I. Chavel, Isoperimetric Inequalities, Cambridge Tracts in Math. 145, Cambridge University Press, Cambridge, 2001. Search in Google Scholar
[7]
H. Chebli,
Sur un théorème de Paley–Wiener associé à la décomposition spectrale d’une opérateur de Sturm–Liouville sur
[8]
H. Chebli,
Théorème de Paley–Wiener associé à un opérateur différentiel singulier sur
[9] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15–53. 10.4310/jdg/1214436699Search in Google Scholar
[10] P. R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401–414. 10.1016/0022-1236(73)90003-7Search in Google Scholar
[11] R. R. Coifman and G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. Math. 31, American Mathematical Society, Providence, 1976. 10.1090/cbms/031Search in Google Scholar
[12]
M. G. Cowling, I. Doust, A. McIntosh and A. Yagi,
Banach space operators with a bounded
[13] A. Erdélyi, Higher Transcendental Functions, Volume I, McGraw–Hill, New York, 1953. Search in Google Scholar
[14] A. Erdélyi, Tables of Integral Transforms, Volume I, McGraw–Hill, New York, 1954. Search in Google Scholar
[15] A. Erdélyi, Tables of Integral Transforms, Volume II, McGraw–Hill, New York, 1954. Search in Google Scholar
[16] G. Gigante, Transference for hypergroups, Collect. Math. 52 (2001), 127–155. Search in Google Scholar
[17] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Math. Monogr., Oxford University Press, Oxford, 1985. Search in Google Scholar
[18] M. Haase, A transference principle for general groups and functional calculus on UMD spaces, Math. Ann. 345 (2009), 245–265. 10.1007/s00208-009-0347-3Search in Google Scholar
[19] E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, Ontario, 1969. Search in Google Scholar
[20] R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math. 18 (1975), 1–101. 10.1016/0001-8708(75)90002-XSearch in Google Scholar
[21] P. D. Lax and R. S. Phillips, The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Funct. Anal. 46 (1982), 280–350. 10.1016/0022-1236(82)90050-7Search in Google Scholar
[22]
A. McIntosh,
Operators which have an
[23] F. G. Mehler, Über eine mit den Kugel- und Cylinderfunctionen verwandte Funktion und ihre Anwendung in der Theorie der Electricitätsvertheilung, Math. Ann. 18 (1881), 161–194. 10.1007/BF01445847Search in Google Scholar
[24] I. N. Sneddon, The Use of Integral Transforms, McGraw–Hill, New York, 1972. Search in Google Scholar
[25] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood–Paley Theory, Ann. of Math. Stud. 63, Princeton University Press, Princeton, 1970. 10.1515/9781400881871Search in Google Scholar
[26] R. S. Strichartz, Analysis of the Laplacian on a complete Riemannian manifold, J. Funct. Anal. 52 (1983), 48–79. 10.1016/0022-1236(83)90090-3Search in Google Scholar
[27]
M. E. Taylor,
[28] M. Taylor, Functions of the Laplace operator on manifolds with lower Ricci and injectivity bounds, Comm. Partial Differential Equations 34 (2009), 1114–1126. 10.1080/03605300902892485Search in Google Scholar
[29] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75–96. 10.1007/BF01902205Search in Google Scholar
[30]
K. Trimèche,
Transformation intégrale de Weyl et théorème de Paley–Wiener associés à un opérateur différentielle singulier sur
[31]
M. Uiterdijk,
A functional calculus for analytic generators of
[32] M. Voit, Positive characters on commutative hypergroups and some applications, Math. Z. 198 (1988), 405–421. 10.1007/BF01184674Search in Google Scholar
[33] E. T. Whittaker and G. N. Watson, A Course in Modern Analysis, 4th ed., Cambridge University Press, London, 1927. Search in Google Scholar
[34] H. Zeuner, One-dimensional hypergroups, Adv. Math. 76 (1989), 1–18. 10.1016/0001-8708(89)90041-8Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Memory-type plate system with nonlinear delay
- Potential theory associated with the Dunkl Laplacian
- Operational calculus and integral transforms for groups with finite propagation speed
- Symmetric positive solutions for the systems of higher-order boundary value problems on time scales
- A sampling theorem for the twisted shift-invariant space
Articles in the same Issue
- Frontmatter
- Memory-type plate system with nonlinear delay
- Potential theory associated with the Dunkl Laplacian
- Operational calculus and integral transforms for groups with finite propagation speed
- Symmetric positive solutions for the systems of higher-order boundary value problems on time scales
- A sampling theorem for the twisted shift-invariant space