Tom ter Elst

Mailing address:

A.F.M. ter Elst
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland 1142
New Zealand

Courier address:

Email address: terelst@math.auckland.ac.nz

Alternatively

Fax number: +64 9 37 37 457
Telephone number: +64 9 923 6901 (direct) or +64 9 3737599 extn 86901

Research Publications

Reviews in MathSciNet

Book

Papers

• The regular part of sectorial forms
  Coauthor: M. Sauter.
  J. Evol. Equ. To appear.

• Diffusion determines the compact manifold.
  Coauthor: W. Arendt.

• From forms to semigroups.
  Coauthor: W. Arendt.
  IWOTA 2010 proceedings. To appear.

• L^infinity-estimates for divergence operators on bad domains.
  Coauthor: J. Rehberg.
  Analysis and Applications. To appear.

• Flows and invariance for degenerate elliptic operators
  Coauthors: D.W. Robinson and A. Sikora.
  J. Austr. Math. Soc. To appear.

• Sectorial forms and degenerate differential operators.
  Coauthor: W. Arendt.
  J. Operator Theory. To appear.

• Diffusion determines the manifold.
  Coauthors: W. Arendt and M. Biegert.
  J. Reine Angew. Math. (Crelle's Journal). To appear.

• The Dirichlet-to-Neumann operator on rough domains.
  Coauthor: W. Arendt.
  Journal of Differential Equations 251, 2100--2124 (2011).

• Partial Gaussian bounds for degenerate differential operators.
  Coauthor: E.-M. Ouhabaz.
  Potential Analysis 35, 175--199 (2011).

• Conservation and invariance properties of submarkovian semigroups.
  Coauthor: D.W. Robinson.
  Journal of the Ramanujan Mathematical Society 24, 285--297 (2009).

• Uniform subellipticity.
  Coauthor: D.W. Robinson.
  J. Operator Theory 62, 125-149 (2009).

• Invariant subspaces of submarkovian semigroups.
  Coauthor: D.W. Robinson.
  J. Evol. Equ. 8, 661-671 (2008).

• Contraction semigroups on $L_\infty({\bf R})$.
  Coauthor: D.W. Robinson.
  In Amann, H., Arendt, W., Hieber, M., Neubrander, F., Nicaise, S. and Below, J. von, eds., Functional Analysis and Evolution Equations. The Gunter Lumer Volume, 209--221. Birkhauser Verlag, Basel, 2007.

• Second-order operators with degenerate coefficients.
  Coauthors: D.W. Robinson, A. Sikora and Y. Zhu.
  Proc. London Math. Soc. 95 (2007), 299-328.

• Small time asymptotics of diffusion processes.
  Coauthors: D.W. Robinson and A. Sikora.
  J. Evol. Equ. 7 (2007), 79--112.

• On multi-commutators and sums of squares of generators of one parameter groups.
  Coauthor: D. Di Giorgio.
  J. Operator Theory 56 (2006), 101--122.

• Dirichlet forms and degenerate elliptic operators. Coauthors: D.W. Robinson, A. Sikora and Y. Zhu.
  In Koelink, E., Neerven, J. van, Pagter, B. de and Sweers, G., eds., Partial Differential Equations and Functional Analysis. Birkhauser.
  Philippe Clement Festschrift. Operator Theory: Advances and Applications, vol. 168 (2006), 73--95.

• Positivity and ellipticity.
  Coauthors: D.W. Robinson and Y. Zhu.
  Proc. Amer. Math. Soc. 134 (2006), 707--714.

• Derivatives of kernels associated to complex subelliptic operators.
  Bull. Austr. Math. Soc. 67 (2003), 393--406.

• Gaussian bounds for complex subelliptic operators on Lie groups of polynomial growth.
  Coauthor: D.W. Robinson.
  Bull. Austr. Math. Soc. 67 (2003), 201--218.

• Asymptotics of semigroup kernels.
  Coauthor: D.W. Robinson.
  In: International Conference on Harmonic Analysis and Related Topics. Editors X.-T. Duong and A. Pryde. Proceedings of the Centre for Mathematics and its Applications, vol. 41, 2003, 128--143.
  

• Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent Lie groups..
  Coauthor: H. Prado.
  Math. Scand. 90 (2002), 251--266.

• Subelliptic operators and Lie groups.
  Coauthor: D.W. Robinson.
  In: National Research Symposium on Geometric Analysis and Applications. Editors A. Isaev, A. Hassell, A. McIntosh and A. Sikora. Proceedings of the Centre for Mathematics and its Applications, vol. 39, 2001, 67--84.
  

• On second-order almost-periodic elliptic operators.
  Coauthors: N. Dungey and D.W. Robinson.
  J. London Math. Soc. 63 (2001), 735--753.
  

• On anomalous asymptotics of heat kernels.
  Coauthor: D.W. Robinson.
  In Lumer, G. and Weis, L., eds., Evolution equations and their applications in physical and life sciences, vol. 215 of Lecture Notes in Pure and Applied Mathematics, 2001, 89--103.

• On second-order periodic elliptic operators in divergence form.
  Coauthors: D.W. Robinson and A. Sikora.
  Math. Z. 238 (2001), 569--637.
  

• Separate and joint Gevrey vectors for representations of Lie groups.
  In: Circumspice. Various papers in and around Mathematics in honor of Arnoud van Rooij, Nijmegen (2001), 221--232.

• Asymptotics of subcoercive semigroups on nilpotent Lie groups.
  Coauthors: N. Dungey, D.W. Robinson and A. Sikora.
  J. Operator Theory 45 (2001), 81--110.

• Second-order subelliptic operators on Lie groups II: real measurable principal coefficients.
  Coauthor: D.W. Robinson.
  In Balakrishnan, A.V., ed., Proceedings for the First International Conference of Semigroups of Operators: Theory and Applications, Newport Beach, California, vol. 42 of Progress in nonlinear differential equations and their applications. Birkhauser Verlag, Basel, 2000, 103--124.

• On anomalous asymptotics of heat kernels on groups of polynomial growth.
  Coauthors: N. Dungey and D.W. Robinson.
  Research Report RANA 00-20.

• Asymptotics of sums of subcoercive operators.
  Coauthors: N. Dungey and D.W. Robinson.
  Coll. Math. 82 (1999), 231--260.
  

• Riesz transforms and Lie groups of polynomial growth.
  Coauthors: D.W. Robinson and A. Sikora.
  J. Funct. Anal. 162 (1999), 14--51.
  

• Reduced heat kernels on homogeneous spaces.
  Coauthor: C.M.P.A. Smulders.
  J. Operator Theory 42 (1999), 269--304.

• Second-order subelliptic operators on Lie groups III: Holder continuous coefficients.
  Coauthor: D.W. Robinson.
  Calc. Var. Partial Differential Equations 8 (1999), 327--363.
  

• Second-order subelliptic operators on Lie groups I: complex uniformly continuous principal coefficients.
  Coauthor: D.W. Robinson.
  Acta Appl. Math. 59 (1999), 299--331.
  

• Local lower bounds on heat kernels.
  Coauthor: D.W. Robinson.
  Positivity 2 (1998), 123--151.
  

• Weighted subcoercive operators on Lie groups.
  Coauthor: D.W. Robinson.
  J. Funct. Anal. 157 (1998), 88--163.
  

• Heat kernels and Riesz transforms on nilpotent Lie groups.
  Coauthors: D.W. Robinson and A. Sikora.
  Coll. Math. 74 (1997), 191--218.

• Second-order strongly elliptic operators on Lie groups with Holder continuous coefficients.
  Coauthor: D.W. Robinson.
  J. Austral. Math. Soc. (Series A) 63 (1997), 297--363.

• High order divergence-form elliptic operators on Lie groups.
  Coauthor: D.W. Robinson.
  Bull. Austral. Math. Soc. 55 (1997) 335--348.

• On Kato's square root problem.
  Coauthor: D.W. Robinson.
  Hokkaido Math. J. 26 (1997), 365--376.

• Gaussian estimates for second order elliptic operators with boundary conditions.
  Coauthor: W. Arendt.
  J. Operator Theory 38 (1997), 87--130.

• Spectral estimates for positive Rockland operators.
  Coauthor: D.W. Robinson.
  In: Algebraic groups and Lie groups; a volume of papers in honour of the late R.W. Richardson. Editor G.I. Lehrer. Australian Mathematical Society Lecture Series 9 (1997), 195--213, Cambridge University Press.

• Analytic elements on Lie groups.
  Coauthor: D.W. Robinson.
  Helv. Phys. Acta 69 (1996), 655--678.

• Elliptic operators on Lie groups.
  Coauthor: D.W. Robinson.
  Acta Appl. Math. 44 (1996), 133--150.
  

• Reduced heat kernels on nilpotent Lie groups.
  Coauthor: D.W. Robinson.
  Commun. Math. Phys. 173 (1995), 475--511.
  

• Subcoercivity and subelliptic operators on Lie groups II: The general case.
  Coauthor: D.W. Robinson.
  Potential Anal. 4 (1995), 205--243.
  

• On positive Rockland operators.
  Coauthors: P. Auscher and D.W. Robinson.
  Coll. Math. 67 (1994), 197--216.

• Weighted strongly elliptic operators on Lie groups.
  Coauthor: D.W. Robinson.
  J. Funct. Anal. 125 (1994), 548--603.
  

• Functional analysis of subelliptic operators on Lie groups.
  Coauthor: D.W. Robinson.
  J. Operator Theory 31 (1994), 277--301.

• $L_p$-regularity of subelliptic operators on Lie groups.
  Coauthors: R.J. Burns and D.W. Robinson.
  J. Operator Theory 31 (1994), 165--187.

• Subcoercivity and subelliptic operators on Lie groups I: Free nilpotent groups.
  Coauthor: D.W. Robinson.
  Potential Anal. 3 (1994), 283--337.
  

• Subelliptic operators on Lie groups: regularity.
  Coauthor: D.W. Robinson.
  J. Austral. Math. Soc. (Series A) 57 (1994), 179--229.

• Subcoercive and subelliptic operators on Lie groups: variable coefficients.
  Coauthor: D.W. Robinson.
  Publ. RIMS. Kyoto Univ. 29 (1993), 745--801.

• Gevrey spaces and their intersections.
  J. Austral. Math. Soc. (Series A) 54 (1993), 263--286.

• On the differential structure of principal series representations.
  J. Operator Theory 28 (1992), 309--320.

• Subelliptic operators on Lie groups.
  Coauthor: D.W. Robinson.
  In: Miniconference on probability and analysis. Editors I. Doust and B. Jefferies. Proceedings of the Centre for Mathematics and its Applications, vol. 29, 1992, 63--72.

• On infinitely differentiable and Gevrey vectors for representations.
  Proc. Amer. Math. Soc. 112 (1991), 795--802.
  

• Antinormal operators.
  Acta Scientiarum Mathematicarum 54 (1990), 151--158.

• Approximation by unitary operators.
  Acta Scientiarum Mathematicarum 54 (1990), 145--149.

• A Gevrey space characterization of certain Gelfand--Shilov spaces $S_\alpha^\beta$.
  Coauthor: S.J.L. van Eijndhoven.
  Proc. Kon. Ned. Akad. Wetensch. A 92 (1989), 175--184.

• Distribution theories based on representations of locally compact Abelian topological groups.
  EUT-Report 88-06, TUE, 1988. 114 pages.

• An algebraic approach to distribution theories.
  Coauthor: J. de Graaf.
  In: Generalized functions, convergence structures and their applications. Editor B. Stankovic. Plenum press, New-York etc., 1988, 171--177.