Associate Professor Ian   Doust
Associate Professor

Associate Professor Ian Doust

Science
Sch of Mathematics & Statistic

BSc (WAust),  MSc (Toronto),  PhD (Edin),  FAustMS

Much of my work is in the area of operator theory and the geometry of Banach spaces. In particular my work has concentrated on the relationships between functional calculus and integral representations for operators, and how this is affected by geometric properties of the spaces on which the operators act. More recently I have been investigating geometric properties of metric spaces.

Phone
9385 7097
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 6113

Publications

  • Journal articles | 2021
    Associate Professor Ian Doust
    Al-shakarchi S; Doust I, 2021, 'AC(σ) spaces for polygonally inscribed curves', Banach Journal of Mathematical Analysis, vol. 15, http://dx.doi.org/10.1007/s43037-020-00110-w
    Journal articles | 2021
    Associate Professor Ian Doust
    Doust I; Robertson G; Stoneham A; Weston A, 2021, 'Distance matrices of subsets of the Hamming cube', Indagationes Mathematicae, vol. 32, pp. 646 - 657, http://dx.doi.org/10.1016/j.indag.2021.01.004
    Journal articles | 2020
    Associate Professor Ian Doust
    Al-shakarchi S; Doust I, 2020, 'Isomorphisms of $AC(σ)$ spaces for linear graphs', Advances in Operator Theory, http://dx.doi.org/10.1007/s43036-020-00053-x
    Journal articles | 2019
    Associate Professor Ian Doust
    Blower G; Brett C; Doust I, 2019, 'Statistical mechanics of the periodic Benjamin-Ono equation', Journal of Mathematical Physics, vol. 60, pp. 093302 - 093302, http://dx.doi.org/10.1063/1.5091737
    Journal articles | 2019
    Associate Professor Ian Doust
    Doust I, 2019, 'A note on positive $\mathcal{AN}$ operators', Bulletin of the Australian Mathematical Society, vol. 100, pp. 129 - 130, http://dx.doi.org/10.1017/S0004972718001296
    Journal articles | 2017
    Associate Professor Ian Doust
    Doust I; Sánchez S; Weston A, 2017, 'Asymptotic negative type properties of finite ultrametric spaces', Journal of Mathematical Analysis and Applications, vol. 446, pp. 1776 - 1793, http://dx.doi.org/10.1016/j.jmaa.2016.09.069
    Journal articles | 2017
    Associate Professor Ian Doust
    Blower G; Doust I, 2017, 'Operational calculus and integral transforms for groups with finite propagation speed', Advances in Pure and Applied Mathematics, vol. 8, pp. 265 - 283, http://dx.doi.org/10.1515/apam-2015-0049
    Journal articles | 2016
    Associate Professor Ian Doust
    Blower G; Brett C; Doust I, 2016, 'Hill's spectral curves and the invariant measure of the periodic KdV equation', Bulletin des Sciences Mathematiques, vol. 140, pp. 864 - 899, http://dx.doi.org/10.1016/j.bulsci.2016.03.005
    Journal articles | 2015
    Associate Professor Ian Doust
    Doust I; Leinert M, 2015, 'Isomorphisms of $AC(σ)$ spaces', Studia Mathematica, vol. 228, pp. 7 - 31, http://dx.doi.org/10.4064/sm228-1-3
    Journal articles | 2014
    Associate Professor Ian Doust
    Blower G; Brett C; Doust I, 2014, 'Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation', Stochastics, vol. 86, pp. 870 - 881, http://dx.doi.org/10.1080/17442508.2014.882924
    Journal articles | 2014
    Associate Professor Ian Doust
    Doust I; Sánchez S; Weston A, 2014, 'A direct proof that ℓ∞(3) has generalized roundness zero', Expositiones Mathematicae, vol. Available online 25 June 2014, pp. 259 - 267, http://dx.doi.org/10.1016/j.exmath.2014.06.001
    Journal articles | 2013
    Associate Professor Ian Doust
    Doust I; Leinert M, 2013, 'Approximation in $AC(σ)$', ArXiv, https://www.researchgate.net/publication/259211398_Approximation_in_ACsigma
    Journal articles | 2012
    Associate Professor Ian Doust
    Caffarelli E; Doust I; Weston A, 2012, 'Metric trees of generalized roundness one', Aequationes Mathematicae, vol. 83, pp. 239 - 256, http://dx.doi.org/10.1007/s00010-011-0108-8
    Journal articles | 2011
    Associate Professor Ian Doust
    Doust IR; Ashton B, 2011, 'AC(σ) operators', Journal of Operator Theory, vol. 65, pp. 255 - 279
    Journal articles | 2010
    Associate Professor Ian Doust
    Doust IR; Terauds V, 2010, 'Extensions of an AC(σ) functional calculus', Journal of Mathematical Analysis and Applications, vol. 362, pp. 100 - 106, http://dx.doi.org/10.1016/j.jmaa.2009.10.001
    Journal articles | 2009
    Associate Professor Ian Doust
    Doust IR; Ashton B, 2009, 'Compact AC(σ) operators', Integral Equations and Operator Theory, vol. 63, pp. 459 - 472, http://dx.doi.org/10.1007/s00020-009-1667-0
    Journal articles | 2008
    Associate Professor Ian Doust
    Doust I; Weston A, 2008, 'Corrigendum to "Enhanced negative type for finite metric trees" [J. Funct. Anal. 254 (2008) 2336-2364] (DOI:10.1016/j.jfa.2008.01.013)', Journal of Functional Analysis, vol. 255, pp. 532 - 533, http://dx.doi.org/10.1016/j.jfa.2008.03.018
    Journal articles | 2008
    Associate Professor Ian Doust
    Doust IR; Weston A, 2008, 'Enhanced negative type for finite metric trees', Journal of Functional Analysis, vol. 254, pp. 2336 - 2364, http://dx.doi.org/10.1016/j.jfa.2008.01.013
    Journal articles | 2008
    Associate Professor Ian Doust
    Doust IR; Lancien G, 2008, 'The spectral type of sums of operators on non-Hilbertian Banach lattices', Journal of the Australian Mathematical Society, vol. 84, pp. 193 - 198, http://dx.doi.org/10.1017/S1446788708000244
    Journal articles | 2006
    Associate Professor Ian Doust
    Ashton B; Doust IR, 2006, 'A comparison of algebras of functions of bounded variation', Proceedings of the Edinburgh Mathematical Society, vol. 49, pp. 575 - 591, http://dx.doi.org/10.1017/S0013091504001130
    Journal articles | 2005
    Associate Professor Ian Doust
    Blower G; Doust IR, 2005, 'A maximal theorem for holomorphic semigroups', Quarterly Journal of Mathematics, vol. 56, pp. 21 - 30, http://dx.doi.org/10.1093/qmath/hah024
    Journal articles | 2005
    Associate Professor Ian Doust
    Ashton BC; Doust IR, 2005, 'Functions of bounded variation on compact subsets of the plane', Studia Mathematica, vol. 169, pp. 163 - 188, http://dx.doi.org/10.4064/sm169-2-5
    Journal articles | 2005
    Associate Professor Ian Doust
    Doust IR; Gillespie TA, 2005, 'Schur multiplier projections on the Von Neumann-Schatten Classes', Journal of Operator Theory, vol. 53, pp. 251 - 272
    Journal articles | 2005
    Associate Professor Ian Doust
    Doust I; Hirschhorn MD; Ho J, 2005, 'Trigonometric Identities, Linear Algebra, and Computer Algebra', The American Mathematical Monthly, vol. 112, pp. 155 - 164, http://dx.doi.org/10.1080/00029890.2005.11920179
    Journal articles | 2005
    Associate Professor Ian Doust
    Doust IR; Hirschhorn MD; Ho J, 2005, 'Trigonometric identities, linear algebra, and computer algebra', American Mathematical Monthly, vol. 112, pp. 155 - 164, http://dx.doi.org/10.2307/30037413
    Journal articles | 2003
    Associate Professor Ian Doust
    Doust IR; Gillespie TA, 2003, 'Well-boundedness of sums and products of operators', Journal of the London Mathematical Society - Second Series, vol. 68, pp. 183 - 192, http://dx.doi.org/10.1112/S0024610703004447
    Journal articles | 2002
    Associate Professor Ian Doust
    Ashton BC; Cheng Q; Doust IR, 2002, 'Some remarks on well-bounded and scalar-type decomposable operators', Houston Journal of Mathematics, vol. 28, pp. 849 - 864
    Journal articles | 2001
    Associate Professor Ian Doust
    Journal articles | 2001
    Associate Professor Ian Doust
    Cheng Q; Doust IR, 2001, 'Well-bounded operators on non-reflexive Banach spaces II', Quaestiones Mathematicae, vol. 24, pp. 183 - 191, http://dx.doi.org/10.1080/16073606.2001.9639206
    Journal articles | 2001
    Associate Professor Ian Doust
    Qingping C; Doust I, 2001, 'Compact well-bounded operators', Glasgow Mathematical Journal, vol. 43, pp. 467 - 475, http://dx.doi.org/10.1017/s0017089501030087
    Journal articles | 2000
    Associate Professor Ian Doust
    Doust IR; Gillespie TA, 2000, 'An example in the theory of AC-operators', Proceedings of the American Mathematical Society, vol. 129, pp. 1453 - 1457
    Journal articles | 1997
    Associate Professor Ian Doust
    Berkson E; Doust IR; Gillespie TA, 1997, 'Properties of AC-operators', ACTA Scientiarum Mathematicarum, pp. 249 - 271
    Journal articles | 1997
    Associate Professor Ian Doust
    Cheng Q; Doust IR, 1997, 'The dual theory of well-bounded operators', Journal of Operator Theory, pp. 35 - 50
    Journal articles | 1996
    Associate Professor Ian Doust
    Cowling MG; Doust IR; Mcintosh A; Yagi A, 1996, 'Banach space operators with bounded H^{infinity} functional calculus', Journal of the Australian Mathematical Society Series A - Pure Mathematics and Statistics, vol. 60, pp. 51 - 89
    Journal articles | 1996
    Associate Professor Ian Doust
    Cheng Q; Doust IR, 1996, 'Well-bounded operators on nonreflexive Banach spaces', Proceedings of the American Mathematical Society, vol. 124, pp. 799 - 808
    Journal articles | 1996
    Associate Professor Ian Doust
    Doust IR; Walden BL, 1996, 'Compact AC-operators', Studia Mathematica, vol. 117, pp. 275 - 287
    Journal articles | 1994
    Associate Professor Ian Doust
    Doust IR; deLaubenfels R, 1994, 'Functional Calculus, Integral Representations, and Banach Space Geometry', Quaestiones Mathematicae, vol. 17, pp. 161 - 171, http://dx.doi.org/10.1080/16073606.1994.9631755
    Journal articles | 1994
    Associate Professor Ian Doust
    Doust I, 1994, 'A weaker condition for normality', Glasgow Mathematical Journal, vol. 36, pp. 249 - 253, http://dx.doi.org/10.1017/S0017089500030792
    Journal articles | 1993
    Associate Professor Ian Doust
    DOUST I; BOZHOU Q, 1993, 'THE SPECTRAL THEOREM FOR WELL-BOUNDED OPERATORS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, vol. 54, pp. 334 - 351, http://dx.doi.org/10.1017/S1446788700031827
    Journal articles | 1992
    Associate Professor Ian Doust
    Doust I; Ricker WJ, 1992, 'Spectral projections for Hermitian operators', Linear Algebra and Its Applications, vol. 175, pp. 75 - 96, http://dx.doi.org/10.1016/0024-3795(92)90303-R
    Journal articles | 1992
    Associate Professor Ian Doust
    Doust IR, 1992, 'Interpolation and extrapolation of well-bounded operators', Journal of Operator Theory, vol. 28, pp. 229 - 250, http://www.theta.ro/
    Journal articles | 1990
    Associate Professor Ian Doust
    Doust IR, 1990, 'A study of counting', Australian Universities' Review, pp. 18 - 19
    Journal articles | 1990
    Associate Professor Ian Doust
    Doust IR, 1990, 'Staffing in Higher Education - Mathematics in the Nineties', Gazette of the Australian Mathematical Society, vol. 17, pp. 43 - 46
    Journal articles | 1989
    Associate Professor Ian Doust
    Doust I, 1989, 'Well-bounded and scalar-type spectral operators on spaces not containing c0', Proceedings of the American Mathematical Society, vol. 105, pp. 367 - 370, http://dx.doi.org/10.1090/S0002-9939-1989-0939963-X
    Journal articles | 1989
    Associate Professor Ian Doust
    Doust I, 1989, 'Well-Bounded And Scalar-Type Spectral Operators On lpSpaces', Journal of the London Mathematical Society, vol. s2-39, pp. 525 - 534, http://dx.doi.org/10.1112/jlms/s2-39.3.525
    Journal articles |
    Associate Professor Ian Doust
    Al-shakarchi S; Doust I, 'Isomorphisms of $BV(σ)$ spaces', , http://arxiv.org/abs/2007.05701v2
    Journal articles |
    Associate Professor Ian Doust
    Amini-Harandi A; Doust I; Robertson G, 'Roundness Properties of Banach spaces', , http://arxiv.org/abs/2105.13739v1
  • Conference Papers | 2017
    Associate Professor Ian Doust
    Doust I; Al-shakarchi S, 2017, 'Isomorphisms of AC(σ) spaces for countable sets', in Böttcher A; Potts D; Stollmann P; Wenzel D (eds.), The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, Springer International Publishing AG, part of Springer Nature, Chemnitz, pp. 193 - 206, presented at International Workshop on Operator Theory and its Applications (IWOTA), Chemnitz, 14 August 2017 - 18 August 2017, http://dx.doi.org/10.1007/978-3-319-75996-8_11
    Conference Papers | 2010
    Associate Professor Ian Doust
    Blower G; Doust IR; Taggart RJ, 2010, 'A maximal theorem for holomorphic semigroups on vector-valued spaces', in Proceedings of the Centre for Mathematics and its applications, Centre for Mathematics and its Applications (CMA), Australian National University, Canberra, pp. 105 - 114, presented at Centre for Mathematics and its Applications (CMA), Australian National University, Canberra, 13 July 2009 - 17 July 2009
    Conference Papers | 2007
    Associate Professor Ian Doust
    Doust IR; Lancien F; Lancien G, 2007, 'Spectral theory for linear operators on L¹ or C(K) spaces', in McIntosh A; Portal P (ed.), Proceedings of the Centre for Mathematics and its Applications, Australian National University, Australian National University, Canberra, pp. 1 - 10, presented at CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis, and Related Topics'', Murramarang, New South Wales, Australia, 21 February 2006 - 24 February 2006
    Conference Papers | 2001
    Associate Professor Ian Doust
    Doust IR, 2001, 'Norms of 0-1 matrices in Cp', in Isaev A; Hassell A; McIntosh A; Sikora A (eds.), Proceedings of the Centre for Mathematics and its Applications, Australian National University, Australian National University, Canberra, pp. 50 - 55, presented at Geometric analysis and applications, Canberra, 26 June 2000 - 30 June 2000
    Conference Papers | 1995
    Associate Professor Ian Doust
    Doust IR, 1995, 'Contractive projections on Lebesgue-Bochner spaces', in Jarosz K (ed.), Lecture Notes in Pure and Applied Mathematics, Dekker, New York, pp. 101 - 109, presented at Function spaces, Edwardsville, Illinois, 17 May 1994 - 20 May 1994
    Conference Proceedings (Editor of) | 1991
    Associate Professor Ian Doust
    Doust I; Jefferies B, (ed.), 1991, 'Miniconference on Probability and Analysis', Austral. Nat. Univ., Canberra, Vol. 29, presented at Miniconference on Probability and Analysis, UNSW, 24 July 1991 - 26 July 1991
    Conference Papers | 1989
    Associate Professor Ian Doust
    Doust IR, 1989, 'An example in the theory of spectral and well-bounded operators', in Doust I; Jefferies B; Li C; McIntosh A (eds.), An example in the theory of spectral and well-bounded operators, Austral. Nat. Univ., Canberra, pp. 83 - 90, presented at Miniconference on Operators in Analysis, 25 September 1989 - 27 September 1989
    Conference Proceedings (Editor of) | 1989
    Associate Professor Ian Doust
    Doust I; Jefferies B; Li C; McIntosh A, (eds.), 1989, 'Miniconference on Operators in Analysis', Austral. Nat. Univ., Canberra, Vol. 24, presented at Miniconference on Operators in Analysis, Macquarie University, Sydney, 25 September 1989 - 27 September 1989
    Conference Proceedings (Editor of) | 1989
    Associate Professor Ian Doust
    Doust IR; Jefferies BRF; Li C; McIntosh A, (eds.), 1989, 'Miniconference on Operators in Analysis. Proceedings of the miniconference held at Macquarie University, Sydney, September 25-27, 1989. Proceedings of the Centre for Mathematical Analysis, Australian National University, 24.', Australian National University, Centre for Mathematical Analysis, Canberra, Macquarie University, Sydney, Vol. 24, presented at Miniconference on Operators in Analysis, Macquarie University, Sydney, 25 September 1989 - 27 September 1989
    Conference Papers | 1988
    Associate Professor Ian Doust
    Doust IR, 1988, 'Contractive projections on Banach spaces', in Fitzpatrick S; Giles J (ed.), Contractive projections on Banach spaces, Austral. Nat. Univ.,, Canberra, pp. 50 - 58, presented at Miniconference on Functional Analysis & Optimization, Canberra, 08 August 1988 - 24 August 1988

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