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 (probably not working any more)
Telephone number: +64 9 923 6901 (direct) or +64 9 3737599 extn 86901

Research Publications

Reviews in MathSciNet

Book

Papers

• On the numerical range of sectorial forms.
  Coauthors: A. Linke and J. Rehberg.
  Pure Appl. Funct. Anal. (2022).

• The diamagnetic inequality for the Dirichlet-to-Neumann operator.
  Coauthor: E.-M. Ouhabaz.
  Bull. Lond. Math. Soc. (2022).

• The generalized Birman-Schwinger principle.
  Coauthors: J. Behrndt and F. Gesztesy.
  Trans. Amer. Math. Soc. 375 (2022), 799--845.

• Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps.
  Coauthor: J. Behrndt.
  J. Spectr. Theory 11 (2021), 1081--1105.

• On the $L^p$-theory for second-order elliptic operators in divergence form with complex coefficients.
  Coauthors: R. Haller-Dintelmann, J. Rehberg and P. Tolksdorf.
  J. Evol. Equ. 21 (2021), 3963--4003.

• H{\"o}lder kernel estimates for Robin operators and Dirichlet-to-Neumann operators.
  Coauthor: M. F. Wong.
  J. Evol. Equ. 20 (2020), 1195--1225.

• The maximum principle via irreducibility.
  Coauthors: W. Arendt and J. Gl{\"u}ck.
  Adv. Nonlinear Stud. 20 (2020), 633--650.

• The Dirichlet-to-Neumann operator on $C(\partial \Omega)$.
  Coauthor: W. Arendt.
  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 20 (2020), 1169--1196.

• Construction of dynamical semigroups by a functional regularisation \`{a} la Kato.
  Coauthor: V. Zagrebnov.
  Theor. Math. Phys. 204 (2020), 875--895.

• Dirichlet-to-Neumann and elliptic operators on $C^{1+\kappa}$-domains: Poisson and Gaussian bounds.
  Coauthor: E.-M. Ouhabaz.
  J. Diff. Equ. 267 (2019), 4224--4273.

• The Dirichlet problem without the maximum principle.
  Coauthor: W. Arendt.
  Annales de l'Institut Fourier 69 (2019), 763--782.

• Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions.
  Coauthor: E.-M. Ouhabaz.
  J. Evol. Eq. 19 (2019), 21--31.

• Operators with continuous kernels.
  Coauthor: W. Arendt.
  Integral Equations Operator Theory 91:45 (2019).

• Consistent operator semigroups and their interpolation.
  Coauthor: J. Rehberg.
  J. Operator Theory 82 (2019), 3--21.

• The Dirichlet-to-Neumann operator for divergence form problems.
  Coauthors: G. Gordon and M. Waurick.
  Ann. Mat. Pura Appl. 198 (2019), 177--203.

• Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator.
  Coauthors: W. Arendt and M. Warma.
  Comm. Partial Differential Equations 43 (2018), 1--24.

• Weak and strong approximation of semigroups on Hilbert spaces.
  Coauthor: R. Chill.
  Integral Equations Operator Theory 90:9 (2018).

• Contractive polynomials in the Volterra operator.
  Coauthor: J. Zemanek.
  Studia Math. 240 (2018), 201--211.

• On maximal parabolic regularity for non-autonomous parabolic operators.
  Coauthors: K. Disser and J. Rehberg.
  J. Differential Equations 262 (2017), 2039--2072.

• On the $L^p$-theory of $C_0$-semigroups associated with second-order elliptic operators with complex singular coefficients.
  Coauthors: V Liskevich, Z. Sobol and H. Vogt.
  Proc. London Maths. Soc. 115 (2017), 693--724.

• On one-parameter Koopman groups.
  Coauthor: M. Lemanczyk.
  Ergodic Theory Dynam. Systems 37 (2017), 1635--1656.

• Ultracontractivity and Eigenvalues: Weyl's Law for the Dirichlet-to-Neumann Operator.
  Coauthor: W. Arendt.
  Integral Equations Operator Theory 88 (2017), 65--89.

• A van der Corput-type lemma for power bounded operators.
  Coauthor: V. M"uller.
  Math. Z. 285 (2017), 143--158.

• H"older estimates for parabolic operators on domains with rough boundary.
  Coauthors: K. Disser and J. Rehberg.
  Ann. Sc. Norm. Super. Pisa Cl. Sci. 17 (2017), 65--79.

• Diffusion determines the compact manifold.
  Coauthor: W. Arendt.
  In Zemanek, J. and Tomilov, Y.}, eds., Etudes op\'eratiorielles}, Banach Center Publ. 112, 2017, 9--14.

• An explicit bound for the Poincare constant on a Lipschitz domain.
  Coauthor: K. Ruddell.
  In Zemanek, J. and Tomilov, Y.}, eds., Etudes op\'eratiorielles}, Banach Center Publ. 112, 2017, 87--97.

• Nonseparability and von Neumann's theorem for domains of unbounded operators.
  Coauthor: M. Sauter.
  J. Operator Theory 75 (2016), 367--386.

• One-dimensional degenerate elliptic operators on $L_p$-spaces with complex coefficients.
  Coauthor: T.D. Do.
  Semigroup Forum 92 (2016), 559--586.

• Dirichlet-to-Neumann maps on bounded Lipschitz domains.
  Coauthor: J. Behrndt.
  J. Differential Equations 259 (2015), 5903--5926

• The form method for $m$-accretive operators.
  Coauthors: M. Sauter and H. Vogt.
  J. Funct. Anal. 269 (2015), 705--744.

• Convergence of the Dirichlet-to-Neumann operator on varying domains
  Coauthor: E.-M. Ouhabaz.
  In: Operator semigroups meet complex analysis, harmonic analysis and mathematical physics.
  Operator Theory: Advances and Applications 250. Birkh"auser, Cham, 2015, 147--154.

• The Dirichlet-to-Neumann operator on exterior domains.
  Coauthor: W. Arendt.
  Potential Anal. 43 (2015), 313--340.

• Partial Gaussian bounds for degenerate differential operators II
  Coauthor: E.-M. Ouhabaz.
  Ann. Sc. Norm. Super. Pisa Cl. Sci. 14 (2015), 37--81.

• Holder estimates for second-order operators on domains with rough boundary.
  Coauthor: J. Rehberg.
  Adv. Diff. Equ. 20 (2015), 299--360.

• Analysis of the heat kernel of the Dirichlet-to-Neumann operator
  Coauthor: E.-M. Ouhabaz.
  J. Funct. Anal. 267 (2014), 4066--4109.

• Parabolic equations with dynamical boundary conditions and source terms on interfaces.
  Coauthors: M. Meyries and J. Rehberg.
  Ann. Mat. Pura Appl. 193 (2014), 1295--1318.

• Analytical aspects of isospectral gongs and drums.
  Coauthors: W. Arendt and J.B. Kennedy.
  Operators and Matrices 8 (2014), 255--277.

• On series of sectorial forms
  Coauthor: C.J.K. Batty.
  J. Evol. Equ. 14 (2014), 29--47.

• The Dirichlet-to-Neumann operator via hidden compactness
  Coauthors: W. Arendt, J.B. Kennedy and M. Sauter.
  J. Funct. Anal. 266 (2014), 1757--1786.

• The regular part of second-order differential sectorial forms with lower-order terms
  Coauthor: M. Sauter.
  J. Evol. Equ. 13 (2013), 737--749.

• Square roots of perturbed subelliptic operators on Lie groups.
  Coauthors: L. Bandara and A. McIntosh.
  Studia Math. 216 (2013), 193--217.

• Partial spectral multipliers and partial Riesz transforms for degenerate operators
  Coauthor: E.-M Ouhabaz.
  Rev. Mat. Iberoamericana 29 (2013), 691--713.

• Diffusion determines the manifold.
  Coauthors: W. Arendt and M. Biegert.
  J. Reine Angew. Math. 667 (2012), 1--25 (Crelle's Journal).

• From forms to semigroups.
  Coauthor: W. Arendt.
  In: Arendt, W., Ball, J.A., Forster, K.-H., Mehrmann, V. and Trunk, C., eds., Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Birkauser, Basel, 47--70 (2012).

• L^infinity-estimates for divergence operators on bad domains.
  Coauthor: J. Rehberg.
  Anal. and Appl. 10 (2012), 207--214.

• Generation and commutation properties of the Volterra operator.
  Coauthor: M. Sauter and J. Zemanek.
  Arch. Math. 99 (2012), 467--479.

• Sectorial forms and degenerate differential operators.
  Coauthor: W. Arendt.
  J. Operator Theory 67 (2012), 33--72.

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

• The regular part of sectorial forms
  Coauthor: M. Sauter.
  J. Evol. Equ. 11 (2011), 907--924.

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

• Flows and invariance for degenerate elliptic operators
  Coauthors: D.W. Robinson and A. Sikora.
  J. Austr. Math. Soc. 90 (2011), 317--339.

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

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

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

• 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.

• 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.

• 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.