Associate Professor Ian Doust

Honorary Associate Professor

Science

School of Mathematics & Statistics

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

E-mail

i.doust@unsw.edu.au

Location

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

Journal articles | 2025

Doust I; Weston A, 2025, 'POLYGONAL EQUALITIES AND p-NEGATIVE TYPE', Proceedings of the American Mathematical Society Series B, 12, pp. 166 - 171,

Journal articles | 2023

Blower G; Doust I, 2023, 'Linear systems, Hankel products and the sinh-Gordon equation', Journal of Mathematical Analysis and Applications, 525, pp. 127140 - 127140,

Journal articles | 2023

Doust I; Leinert M; Stoneham A, 2023, 'Approximation in AC(σ)', Banach Journal of Mathematical Analysis, 17, pp. 5,

Journal articles | 2023

Doust I; Leinert M; Stoneham A, 2023, 'The Banach Algebras AC(σ) and BV(σ)', Results in Mathematics, 78, pp. 20,

Journal articles | 2022

Doust I; Wolf R, 2022, 'A PROBLEM ON DISTANCE MATRICES OF SUBSETS OF THE HAMMING CUBE', Proceedings of the American Mathematical Society Series B, 9, pp. 125 - 134,

Journal articles | 2021

Al-Shakarchi S; Doust I, 2021, 'ISOMORPHISMS OF BV (σ) SPACES', Operators and Matrices, 15, pp. 1581 - 1596,

Journal articles | 2021

Al-shakarchi S; Doust I, 2021, 'AC(σ) spaces for polygonally inscribed curves', Banach Journal of Mathematical Analysis, 15, pp. 31,

Journal articles | 2021

Amini-Harandi A; Doust I; Robertson G, 2021, 'Roundness properties of Banach spaces', Journal of Functional Analysis, 281, pp. 109230,

Journal articles | 2021

Doust I; Robertson G; Stoneham A; Weston A, 2021, 'Distance matrices of subsets of the Hamming cube', Indagationes Mathematicae, 32, pp. 646 - 657,

Journal articles | 2020

Al-shakarchi S; Doust I, 2020, 'Isomorphisms of $AC(σ)$ spaces for linear graphs', Advances in Operator Theory, 5,

Journal articles | 2019

Blower G; Brett C; Doust I, 2019, 'Statistical mechanics of the periodic Benjamin-Ono equation', Journal of Mathematical Physics, 60, pp. 093302,

Journal articles | 2019

Doust I, 2019, 'A NOTE ON POSITIVE AN OPERATORS', Bulletin of the Australian Mathematical Society, 100, pp. 129 - 130,

Journal articles | 2017

Blower G; Doust I, 2017, 'Operational calculus and integral transforms for groups with finite propagation speed', Advances in Pure and Applied Mathematics, 8, pp. 265 - 283,

Journal articles | 2017

Doust I; Sánchez S; Weston A; Sanchez S, 2017, 'Asymptotic negative type properties of finite ultrametric spaces', Journal of Mathematical Analysis and Applications, 446, pp. 1776 - 1793,

Journal articles | 2016

Blower G; Brett C; Doust I, 2016, 'Hill's spectral curves and the invariant measure of the periodic KdV equation', Bulletin Des Sciences Mathematiques, 140, pp. 864 - 899,

Journal articles | 2015

Doust I; Leinert M, 2015, 'Isomorphisms of AC(σ) spaces', Studia Mathematica, 228, pp. 7 - 31,

Journal articles | 2014

Blower G; Brett C; Doust I, 2014, 'Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation', Stochastics, 86, pp. 870 - 881,

Journal articles | 2014

Doust I; Sánchez S; Weston A, 2014, 'A direct proof that ℓ∞(3) has generalized roundness zero', Expositiones Mathematicae, Available online 25 June 2014,

Journal articles | 2013

Doust I; Leinert M, 2013, 'Approximation in $AC(σ)$', ArXiv,

Journal articles | 2012

Caffarelli E; Doust I; Weston A, 2012, 'Metric trees of generalized roundness one', Aequationes Mathematicae, 83, pp. 239 - 256,

Journal articles | 2011

Doust IR; Ashton B, 2011, 'AC(σ) operators', Journal of Operator Theory, 65, pp. 255 - 279

Journal articles | 2010

Doust IR; Terauds V, 2010, 'Extensions of an AC(σ) functional calculus', Journal of Mathematical Analysis and Applications, 362, pp. 100 - 106,

Journal articles | 2009

Doust IR; Ashton B, 2009, 'Compact AC(σ) operators', Integral Equations and Operator Theory, 63, pp. 459 - 472

Journal articles | 2008

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, 255, pp. 532 - 533,

Journal articles | 2008

Doust IR; Lancien G, 2008, 'The spectral type of sums of operators on non-Hilbertian Banach lattices', Journal of the Australian Mathematical Society, 84, pp. 193 - 198

Journal articles | 2008

Doust IR; Weston A, 2008, 'Enhanced negative type for finite metric trees', Journal of Functional Analysis, 254, pp. 2336 - 2364

Journal articles | 2006

Ashton B; Doust IR, 2006, 'A comparison of algebras of functions of bounded variation', Proceedings of the Edinburgh Mathematical Society, 49, pp. 575 - 591

Journal articles | 2005

Ashton BC; Doust IR, 2005, 'Functions of bounded variation on compact subsets of the plane', Studia Mathematica, 169, pp. 163 - 188

Journal articles | 2005

Blower G; Doust IR, 2005, 'A maximal theorem for holomorphic semigroups', Quarterly Journal of Mathematics, 56, pp. 21 - 30

Journal articles | 2005

Doust I; Hirschhorn MD; Ho J, 2005, 'Trigonometric Identities, Linear Algebra, and Computer Algebra', The American Mathematical Monthly, 112, pp. 155 - 164,

Journal articles | 2005

Doust IR; Gillespie TA, 2005, 'Schur multiplier projections on the Von Neumann-Schatten Classes', Journal of Operator Theory, 53, pp. 251 - 272

Journal articles | 2005

Doust IR; Hirschhorn MD; Ho J, 2005, 'Trigonometric identities, linear algebra, and computer algebra', American Mathematical Monthly, 112, pp. 155 - 164,

Journal articles | 2003

Doust IR; Gillespie TA, 2003, 'Well-boundedness of sums and products of operators', Journal of the London Mathematical Society - Second Series, 68, pp. 183 - 192

Journal articles | 2002

Ashton BC; Cheng Q; Doust IR, 2002, 'Some remarks on well-bounded and scalar-type decomposable operators', Houston Journal of Mathematics, 28, pp. 849 - 864

Journal articles | 2001

Cheng Q; Doust IR, 2001, 'Well-bounded operators on non-reflexive Banach spaces II', Quaestiones Mathematicae, pp. 183 - 191

Journal articles | 2001

Cheng QP; Doust I, 2001, 'Compact well-bounded operators', GLASGOW MATHEMATICAL JOURNAL, 43, pp. 467 - 475

Journal articles | 2001

Qingping C; Doust I, 2001, 'Compact well-bounded operators', Glasgow Mathematical Journal, 43, pp. 467 - 475,

Journal articles | 2000

Doust IR; Gillespie TA, 2000, 'An example in the theory of AC-operators', Proceedings of the American Mathematical Society, 129, pp. 1453 - 1457

Journal articles | 1997

Berkson E; Doust IR; Gillespie TA, 1997, 'Properties of AC-operators', ACTA Scientiarum Mathematicarum, pp. 249 - 271

Journal articles | 1997

Cheng Q; Doust IR, 1997, 'The dual theory of well-bounded operators', Journal of Operator Theory, pp. 35 - 50

Journal articles | 1996

Cheng Q; Doust IR, 1996, 'Well-bounded operators on nonreflexive Banach spaces', Proceedings of the American Mathematical Society, 124, pp. 799 - 808

Journal articles | 1996

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, pp. 51 - 89

Journal articles | 1996

Doust IR; Walden BL, 1996, 'Compact AC-operators', Studia Mathematica, 117, pp. 275 - 287

Journal articles | 1994

Doust I, 1994, 'A weaker condition for normality', Glasgow Mathematical Journal, 36, pp. 249 - 253,

Journal articles | 1994

Doust IR; deLaubenfels R, 1994, 'Functional Calculus, Integral Representations, and Banach Space Geometry', Quaestiones Mathematicae, 17, pp. 161 - 171,

Journal articles | 1993

DOUST I; BOZHOU Q, 1993, 'THE SPECTRAL THEOREM FOR WELL-BOUNDED OPERATORS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 54, pp. 334 - 351,

Journal articles | 1992

Doust I; Ricker WJ, 1992, 'Spectral projections for Hermitian operators', Linear Algebra and Its Applications, 175, pp. 75 - 96,

Journal articles | 1992

Doust IR, 1992, 'Interpolation and extrapolation of well-bounded operators', Journal of Operator Theory, 28, pp. 229 - 250,

Journal articles | 1990

Doust IR, 1990, 'A study of counting', Australian Universities' Review, pp. 18 - 19

Journal articles | 1990

Doust IR, 1990, 'Staffing in Higher Education - Mathematics in the Nineties', Gazette of the Australian Mathematical Society, 17, pp. 43 - 46

Journal articles | 1989

Doust I, 1989, 'Well-Bounded And Scalar-Type Spectral Operators On lpSpaces', Journal of the London Mathematical Society, s2-39, pp. 525 - 534,

Journal articles | 1989

Doust I, 1989, 'Well-bounded and scalar-type spectral operators on spaces not containing c0', Proceedings of the American Mathematical Society, 105, pp. 367 - 370,
Preprints | 2024

Blower G; Doust I, 2024, Linear systems, spectral curves and determinants,

Preprints | 2023

Doust I; Stoneham A, 2023, Tietze type extensions for absolutely continuous functions in the plane, ,

Preprints | 2022

Blower G; Doust I, 2022, Linear systems, Hankel products and the sinh-Gordon equation,

Preprints | 2022

Doust I; Leinert M; Stoneham A, 2022, The Banach algebras $AC(σ)$ and $BV(σ)$,

Preprints | 2022

Blower G; Doust I, 2022, Linear systems, Hankel products and the sinh-Gordon equation,

Preprints | 2021

Doust I; Wolf R, 2021, A problem on distance matrices of subsets of the Hamming cube,

Preprints | 2020

Al-shakarchi S; Doust I, 2020, $AC(σ)$ spaces for polygonally inscribed curves,

Preprints | 2020

Doust I; Robertson G; Stoneham A; Weston A, 2020, Distance matrices of subsets of the Hamming cube,

Preprints | 2019

Blower G; Brett C; Doust I, 2019, Statistical Mechanics of the Periodic Benjamin-Ono Equation,

Preprints | 2018

Al-shakarchi S; Doust I, 2018, Isomorphisms of $AC(σ)$ spaces for linear graphs,

Preprints | 2018

Doust I, 2018, A note on positive $\mathcal{AN}$ operators,

Conference Papers | 2017

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,

Preprints | 2017

Doust I; Al-shakarchi S, 2017, Isomorphisms of $AC(σ)$ spaces for countable sets,

Preprints | 2015

Blower G; Doust I, 2015, Operational calculus and integral transforms for groups with finite propagation speed,

Preprints | 2014

Blower G; Brett C; Doust I, 2014, Hill's Spectral Curves and the Invariant Measure of the Periodic KdV Equation,

Preprints | 2014

Doust I; Sánchez S; Weston A, 2014, A direct proof that $\ell_\infty^{(3)}$ has generalized roundness zero,

Preprints | 2013

Blower G; Brett C; Doust I, 2013, Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation,

Preprints | 2013

Doust I; Leinert M, 2013, Approximation in $AC(σ)$,

Preprints | 2013

Doust I; Leinert M, 2013, Isomorphisms of $AC(\sigma)$ spaces,

Preprints | 2013

Doust I; Leinert M, 2013, Isomorphisms of $AC(σ)$ spaces,

Preprints | 2013

Doust I; Sánchez S; Weston A, 2013, The asymptotic enhanced negative type of finite ultrametric spaces,

Preprints | 2010

Caffarelli E; Doust I; Weston A, 2010, Metric trees of generalized roundness one,

Conference Papers | 2009

Blower G; Doust IR; Taggart RJ, 2009, '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

Preprints | 2008

Ashton B; Doust I, 2008, Compact $AC(\sigma)$ operators,

Preprints | 2008

Doust I; Terauds V, 2008, Extensions of an $AC(\sigma)$ functional calculus,

Preprints | 2007

Doust I; Weston A, 2007, Enhanced negative type for finite metric trees,

Conference Papers | 2006

Doust IR; Lancien F; Lancien G, 2006, '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 | 2000

Doust IR, 2000, '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 | 1994

Doust IR, 1994, '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

Doust I; Jefferies B, (ed.), 1991, 'Miniconference on Probability and Analysis', Austral. Nat. Univ., Canberra, Vol. 29, presented at Miniconference on Probability and Analysis, ��¼�, 24 July 1991 - 26 July 1991

Conference Papers | 1989

Doust IR, 1989, 'An example in the theory of spectral and well-bounded operators', in Doust I; Jefferies B; Li C; McIntosh A (eds.), 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

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

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

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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