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1999 | 82 | 2 | 231-260
Tytuł artykułu

Asymptotics of sums of subcoercive operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel and the kernel corresponding to the lowest order homogeneous component. We also prove boundedness of a range of Riesz transforms with the range again determined by the highest and lowest orders. Finally we analyze similar properties on general groups of polynomial growth and establish positive results for local direct products of compact and nilpotent groups.
Słowa kluczowe
Rocznik
Tom
82
Numer
2
Strony
231-260
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-03-02
poprawiono
1999-07-05
Twórcy
autor
  • Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia
  • Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
  • Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia
Bibliografia
  • [ADM] Albrecht, D., Duong, X., and McIntosh, A., Operator theory and harmonic analysis, in: Instructional Workshop on Analysis and Geometry, Part III, Proc. Centre Math. Appl. 34, Australian National Univ., Canberra, 1996, 77-136.
  • [BaD] Barbatis, G., and Davies, E. B., Sharp bounds on heat kernels of higher order uniformly elliptic operators, J. Operator Theory 36 (1996), 179-198.
  • [Dav] Davies, E. B., One-Parameter Semigroups, London Math. Soc. Monographs 15, Academic Press, London, 1980.
  • [Dun] Dungey, N., Higher order operators and Gaussian bounds on Lie groups of polynomial growth, Research Report MRR 053-98, Australian National Univ., Canberra, 1998.
  • [DERS] Dungey, N., Elst, A. F. M. ter, Robinson, D. W., and Sikora, A., Asymptotics of subcoercive semigroups on nilpotent Lie groups, J. Operator Theory (1999), to appear.
  • [ElR1] Elst, A. F. M. ter, and Robinson, D. W., Subcoercivity and subelliptic operators on Lie groups I: Free nilpotent groups, Potential Anal. 3 (1994), 283-337.
  • [ElR2] Elst, A. F. M. ter, and Robinson, D. W., Weighted strongly elliptic operators on Lie groups, J. Funct. Anal. 125 (1994), 548-603.
  • [ElR3] Elst, A. F. M. ter, and Robinson, D. W., Subcoercivity and subelliptic operators on Lie groups II: The general case, Potential Anal. 4 (1995), 205-243.
  • [ElR4] Elst, A. F. M. ter, and Robinson, D. W., Weighted subcoercive operators on Lie groups, J. Funct. Anal. 157 (1998), 88-163.
  • [ElR5] Elst, A. F. M. ter, and Robinson, D. W., Local lower bounds on heat kernels, Positivity 2 (1998), 123-151.
  • [ERS1] Elst, A. F. M. ter, Robinson, D. W., and Sikora, A., Heat kernels and Riesz transforms on nilpotent Lie groups, Colloq. Math. 74 (1997), 191-218.
  • [ERS2] Elst, A. F. M. ter, Robinson, D. W., and Sikora, A., Riesz transforms and Lie groups of polynomial growth, J. Funct. Anal. 162 (1999), 14-51.
  • [NRS] Nagel, A., Ricci, F., and Stein, E. M., Harmonic analysis and fundamental solutions on nilpotent Lie groups, in: C. Sadosky (ed.), Analysis and Partial Differential Equations, Lecture Notes in Pure and Appl. Math. 122, Dekker, New York, 1990, 249-275.
  • [Rob] Robinson, D. W., Elliptic Operators and Lie Groups, Oxford Math. Monographs, Oxford Univ. Press, Oxford, 1991.
  • [VSC] Varopoulos, N. T., Saloff-Coste, L., and Coulhon, T., Analysis and Geometry on Groups, Cambridge Tracts in Math. 100, Cambridge Univ. Press, Cambridge, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv82i2p231bwm
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