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Dr Denis Potapov
Senior Lecturer

Dr Denis Potapov

Science
School of Mathematics & Statistics

Research interests:   Noncommutative analysis and noncommutative integration; perturbation theory; noncommutative and vector-valued harmonic analysis.

Best publications:  (i) Operator-Lipschitz functions in Schatten-von Neumann classes --- Acta Math. (ii) Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators --- Adv. Math. (iii) Unbounded Fredholm modules and double operator integrals --- Crelle J.

 

 
Phone
9385 7003
E-mail
d (dot) potapov (at) unsw (dot) edu (dot) au
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre East Wing, Room 6111
  • Book Chapters | 2019
    Potapov D; Sukochev F; Vella D; Zanin D, 2019, 'A residue formula for locally compact noncommutative manifolds', in Positivity and Noncommutative Analysis, pp. 471 - 510, http://dx.doi.org/10.1007/978-3-030-10850-2_24
  • Journal articles | 2022
    Carey A; Levitina G; Potapov D; Sukochev F, 2022, 'The Witten index and the spectral shift function', Reviews in Mathematical Physics, vol. 34, http://dx.doi.org/10.1142/S0129055X22500118
    Journal articles | 2019
    Aleksandrov AB; Peller VV; Potapov DS, 2019, 'On a Trace Formula for Functions of Noncommuting Operators', Mathematical Notes, vol. 106, pp. 481 - 487, http://dx.doi.org/10.1134/S0001434619090189
    Journal articles | 2019
    Caspers M; Potapov D; Sukochev F; Zanin D, 2019, 'WEAK TYPE COMMUTATOR AND LIPSCHITZ ESTIMATES: RESOLUTION OF THE NAZAROV-PELLER CONJECTURE', AMERICAN JOURNAL OF MATHEMATICS, vol. 141, pp. 593 - 610, http://dx.doi.org/10.1353/ajm.2019.0019
    Journal articles | 2019
    Potapov D; Sukochev F; Tomskova A; Zanin D, 2019, 'FrÉchet differentiability of the norm of Lp-spaces associated with arbitrary von Neumann algebras', Transactions of the American Mathematical Society, vol. 371, pp. 7493 - 7532, http://dx.doi.org/10.1090/tran/7215
    Journal articles | 2019
    Александров АБ; Aleksandrov AB; Пеллер ВВ; Peller VV; Потапов ДС; Potapov DS, 2019, 'О формуле следов для функций от некоммутирующих операторов', Matematicheskie Zametki, vol. 106, pp. 483 - 490, http://dx.doi.org/10.4213/mzm12259
    Journal articles | 2018
    Carey A; Gesztesy F; Kaad J; Levitina G; Nichols R; Potapov D; Sukochev F, 2018, 'On the Global Limiting Absorption Principle for Massless Dirac Operators', Annales Henri Poincare, vol. 19, pp. 1993 - 2019, http://dx.doi.org/10.1007/s00023-018-0675-5
    Journal articles | 2017
    Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2017, 'On the Witten index in terms of spectral shift functions', Journal d'Analyse Mathematique, vol. 132, pp. 1 - 61, http://dx.doi.org/10.1007/s11854-017-0003-x
    Journal articles | 2017
    Potapov D; Skripka A; Sukochev F; Tomskova A, 2017, 'Multilinear Schur multipliers and Schatten properties of operator Taylor remainders', Advances in Mathematics, vol. 320, pp. 1063 - 1098, http://dx.doi.org/10.1016/j.aim.2017.09.012
    Journal articles | 2016
    Carey A; Gesztesy F; Grosse H; Levitina G; Potapov D; Sukochev F; Zanin D, 2016, 'Trace formulas for a class of non-Fredholm operators: A review', Reviews in Mathematical Physics, vol. 28, http://dx.doi.org/10.1142/S0129055X16300028
    Journal articles | 2016
    Carey A; Gesztesy F; Levitina G; Nichols R; Potapov D; Sukochev F, 2016, 'Double operator integral methods applied to continuity of spectral shift functions', Journal of Spectral Theory, vol. 6, pp. 747 - 779, http://dx.doi.org/10.4171/JST/140
    Journal articles | 2016
    Carey A; Gesztesy F; Levitina G; Potapov D; Sukochev F; Zanin D, 2016, 'On index theory for non-Fredholm operators: A (1 + 1)-dimensional example', Mathematische Nachrichten, vol. 289, pp. 575 - 609, http://dx.doi.org/10.1002/mana.201500065
    Journal articles | 2016
    Coine C; Le Merdy C; Potapov D; Sukochev F; Tomskova A, 2016, 'Peller's problem concerning Koplienko–Neidhardt trace formulae: the unitary case', Journal of Functional Analysis, vol. 271, pp. 1747 - 1763, http://dx.doi.org/10.1016/j.jfa.2016.05.015
    Journal articles | 2016
    Coine C; Le Merdy C; Potapov D; Sukochev F; Tomskova A, 2016, 'Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae', Proceedings of the London Mathematical Society, vol. 113, pp. 113 - 139, http://dx.doi.org/10.1112/plms/pdw024
    Journal articles | 2016
    Potapov D; Skripka A; Sukochev F, 2016, 'Functions of unitary operators: Derivatives and trace formulas', Journal of Functional Analysis, vol. 270, pp. 2048 - 2072, http://dx.doi.org/10.1016/j.jfa.2016.01.001
    Journal articles | 2015
    Caspers M; Potapov D; Sukochev F; Zanin D, 2015, 'Weak type estimates for the absolute value mapping', Journal of Operator Theory, vol. 73, pp. 361 - 384, http://dx.doi.org/10.7900/jot.2013dec20.2021
    Journal articles | 2015
    Potapov D; Skripka A; Sukochev F, 2015, 'Trace formulas for resolvent comparable operators', Advances in Mathematics, vol. 272, pp. 630 - 651, http://dx.doi.org/10.1016/j.aim.2014.12.016
    Journal articles | 2015
    Potapov D; Sukochev F; Tomskova A, 2015, 'On the Arazy conjecture concerning Schur multipliers on Schatten ideals', Advances in Mathematics, vol. 268, pp. 404 - 422, http://dx.doi.org/10.1016/j.aim.2014.09.021
    Journal articles | 2015
    Potapov D; Sukochev F; Usachev A; Zanin D, 2015, 'Singular traces and perturbation formulae of higher order', Journal of Functional Analysis, vol. 269, pp. 1441 - 1481, http://dx.doi.org/10.1016/j.jfa.2015.04.019
    Journal articles | 2014
    Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2014, 'A Jost-Pais-Type Reduction of Fredholm Determinants and Some Applications', Integral Equations and Operator Theory, vol. 79, pp. 389 - 447, http://dx.doi.org/10.1007/s00020-014-2150-0
    Journal articles | 2014
    Caspers M; Montgomery-Smith S; Potapov D; Sukochev F, 2014, 'The best constants for operator Lipschitz functions on Schatten classes', Journal of Functional Analysis, vol. 267, pp. 3557 - 3579, http://dx.doi.org/10.1016/j.jfa.2014.08.018
    Journal articles | 2014
    Potapov D; Skripka A; Sukochev F, 2014, 'Functions of unitary operators: Derivatives and trace formulas', Journal of Functional Analysis, http://dx.doi.org/10.1016/j.jfa.2016.01.001
    Journal articles | 2014
    Potapov D; Skripka A; Sukochev F, 2014, 'Higher-order spectral shift for contractions', Proceedings of the London Mathematical Society, vol. 108, pp. 327 - 349, http://dx.doi.org/10.1112/plms/pdt024
    Journal articles | 2014
    Potapov D; Sukochev F, 2014, 'Frechet differentiability of S-p norms', ADVANCES IN MATHEMATICS, vol. 262, pp. 436 - 475, http://dx.doi.org/10.1016/j.aim.2014.05.011
    Journal articles | 2014
    Potapov D; Sukochev F; Tomskova A; Zanin D, 2014, 'Fréchet differentiability of the norm of Lp-spaces associated with arbitrary von Neumann algebras', Comptes Rendus Mathematique, vol. 352, pp. 923 - 927, http://dx.doi.org/10.1016/j.crma.2014.09.017
    Journal articles | 2014
    Potapov D; Sukochev F; Zanin D, 2014, 'Krein's trace theorem revisited', Journal of Spectral Theory, vol. 4, pp. 415 - 430, http://dx.doi.org/10.4171/JST/75
    Journal articles | 2013
    Caspers ; Potapov D; Sukochev F, 2013, 'The Walsh basis in the Lp-spaces of hyperfinite IIIλ factors, 0', Journal of Mathematical Analysis and Applications, vol. 408, pp. 154 - 164, http://dx.doi.org/10.1016/j.jmaa.2013.06.003
    Journal articles | 2013
    Kalton N; Lord S; Potapov D; Sukochev F, 2013, 'Traces of compact operators and the noncommutative residue', Advances in Mathematics, vol. 235, pp. 1 - 55, http://dx.doi.org/10.1016/j.aim.2012.11.007
    Journal articles | 2013
    Potapov D; Skripka A; Sukochev F, 2013, 'On Hilbert-Schmidt compatibility', Operators and Matrices, vol. 7, pp. 1 - 33, http://dx.doi.org/10.7153/oam-07-01
    Journal articles | 2013
    Potapov D; Skripka A; Sukochev F, 2013, 'Spectral shift function of higher order', Inventiones Mathematicae, vol. 193, pp. 501 - 538, http://dx.doi.org/10.1007/s00222-012-0431-2
    Journal articles | 2012
    Kissin EV; Potapov DS; Shulman VS; Sukochev FA, 2012, 'Operator smoothness in Schatten norms for functions of several variables: Lipschitz conditions, differentiability and unbounded derivations', Proceedings of the London Mathematical Society, 3rd Series, vol. 105, pp. 661 - 702, http://dx.doi.org/10.1112/plms/pds014
    Journal articles | 2012
    Potapov D; Sukochev F, 2012, 'Koplienko Spectral Shift Function on the Unit Circle', Communications in Mathematical Physics, vol. 309, pp. 693 - 702, http://dx.doi.org/10.1007/s00220-011-1338-2
    Journal articles | 2012
    Potapov D; Sukochev F; Xu Q, 2012, 'On the vector-valued Littlewood-Paley-Rubio de Francia inequality', Revista Matematica Iberoamericana, vol. 28, pp. 839 - 856, http://dx.doi.org/10.4171/RMI/693
    Journal articles | 2011
    Aleksandrov A; Peller V; Potapov D; Sukochev F, 2011, 'Functions of normal operators under perturbations', Advances in Mathematics, vol. 226, pp. 5216 - 5251, http://dx.doi.org/10.1016/j.aim.2011.01.008
    Journal articles | 2011
    Dirksen S; De Pagter B; Potapov D; Sukochev F, 2011, 'Rosenthal inequalities in noncommutative symmetric spaces', Journal of Functional Analysis, vol. 261, pp. 2890 - 2925, http://dx.doi.org/10.1016/j.jfa.2011.07.015
    Journal articles | 2011
    Kissin E; Potapov D; Shulman V; Sukochev F, 2011, 'Lipschitz functions, Schatten ideals, and unbounded derivations', Functional Analysis and Its Applications, vol. 45, pp. 157 - 159, http://dx.doi.org/10.1007/s10688-011-0018-5
    Journal articles | 2011
    Potapov D; Sukochev F, 2011, 'Operator-Lipschitz functions in Schatten-von Neumann classes', ACTA Mathematica, vol. 207, pp. 375 - 389, http://dx.doi.org/10.1007/s11511-012-0072-8
    Journal articles | 2011
    Potapov D; Sukochev F, 2011, 'The Haar system in the preduals of hyperfinite factors', Canadian Mathematical Bulletin, vol. 54, pp. 347 - 363, http://dx.doi.org/10.4153/CMB-2011-007-7
    Journal articles | 2010
    Aleksandrov A; Peller V; Potapov D; Sukochev F, 2010, 'Functions of perturbed normal operators', Comptes Rendus Mathematique, vol. 348, pp. 553 - 558, http://dx.doi.org/10.1016/j.crma.2010.04.015
    Journal articles | 2010
    Lord S; Potapov D; Sukochev F, 2010, 'Measures from Dixmier traces and zeta functions', Journal of Functional Analysis, vol. 259, pp. 1915 - 1949, http://dx.doi.org/10.1016/j.jfa.2010.06.012
    Journal articles | 2010
    Potapov D; Sukochev F, 2010, 'Double operator integrals and submajorization', Mathematical Modelling of Natural Phenomena (MMNP), vol. 5, pp. 317 - 339, http://dx.doi.org/10.1051/mmnp/20105401
    Journal articles | 2009
    Carey AL; Potapov D; Sukochev F, 2009, 'Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators', Advances in Mathematics, vol. 222, pp. 1809 - 1849, http://dx.doi.org/10.1016/j.aim.2009.06.020
    Journal articles | 2009
    Potapov D; Sukochev F, 2009, 'Unbounded Fredholm modules and double operator integrals', Journal fur die Reine und Angewandte Mathematik, vol. 626, pp. 159 - 185, http://dx.doi.org/10.15.15/CRELLE.2008
    Journal articles | 2009
    Potapov D; Sukochev F, 2009, 'Unbounded Fredholm modules and double operator integrals', Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2009, http://dx.doi.org/10.1515/crelle.2009.006
    Journal articles | 2008
    Potapov D; Sukochev F, 2008, 'Lipschitz and commutator estimates in symmetric operator spaces', Journal of Operator Theory, vol. 59, pp. 211 - 234
    Journal articles | 2007
    Potapov D; Sukochev F, 2007, 'Non-(quantum) differentiable C1-functions in the spaces with trivial Boyd indices', Integral Equations and Operator Theory, vol. 57, pp. 247 - 261, http://dx.doi.org/10.1007/s00020-006-1468-7
    Journal articles | 2006
    Potapov D; Hytonen TP, 2006, 'Vector-valued multiplier theorems of Coifman-Rubio de Francia-Semmes type', Archiv der Mathematik, vol. 87, pp. 245 - 254, http://dx.doi.org/10.1007/s00013-006-1751-5
    Journal articles | 2005
    Sukochev F; Potapov D, 2005, 'A vector-valued Littlewood-Paley theorem for an arbitrary set of intervals and its applications', Comptes Rendus de l`Academie des Sciences de L Urss, vol. 404, pp. 598 - 600
  • Preprints | 2021
    Carey A; Levitina G; Potapov D; Sukochev F, 2021, The Witten index and the spectral shift function, http://dx.doi.org/10.48550/arxiv.2101.06812
    Preprints | 2019
    Aleksandrov AB; Peller VV; Potapov DS, 2019, On a trace formula for functions of noncommuting operators, http://dx.doi.org/10.48550/arxiv.1901.09495
    Preprints | 2017
    Carey A; Gesztesy F; Kaad J; Levitina G; Nichols R; Potapov D; Sukochev F, 2017, On the Global Limiting Absorption Principle for Massless Dirac Operators, http://dx.doi.org/10.48550/arxiv.1711.01029
    Preprints | 2016
    Carey A; Gesztesy F; Grosse H; Levitina G; Potapov D; Sukochev F; Zanin D, 2016, Trace Formulas for a Class of non-Fredholm Operators: A Review, http://dx.doi.org/10.48550/arxiv.1610.04954
    Preprints | 2016
    Potapov D; Sukochev F; Usachev A; Zanin D, 2016, Singular traces and perturbation formulae of higher order, http://dx.doi.org/10.48550/arxiv.1612.04511
    Preprints | 2015
    Carey A; Gesztesy F; Levitina G; Nichols R; Potapov D; Sukochev F, 2015, Double operator integral methods applied to continuity of spectral shift functions, http://dx.doi.org/10.48550/arxiv.1511.07998
    Preprints | 2015
    Carey A; Gesztesy F; Levitina G; Potapov D; Sukochev F; Zanin D, 2015, On Index Theory for Non-Fredholm Operators: A $(1+1)$-Dimensional Example, http://dx.doi.org/10.48550/arxiv.1509.01356
    Preprints | 2015
    Caspers M; Potapov D; Sukochev F; Zanin D, 2015, Weak type commutator and Lipschitz estimates: resolution of the Nazarov-Peller conjecture, http://dx.doi.org/10.48550/arxiv.1506.00778
    Preprints | 2015
    Coine C; Merdy CL; Potapov D; Sukochev F; Tomskova A, 2015, Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case, http://dx.doi.org/10.48550/arxiv.1509.00616
    Preprints | 2015
    Coine C; Merdy CL; Potapov D; Sukochev F; Tomskova A, 2015, Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae, http://dx.doi.org/10.48550/arxiv.1504.03843
    Preprints | 2014
    Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2014, A Jost-Pais-type reduction of Fredholm determinants and some applications, http://dx.doi.org/10.48550/arxiv.1404.0739
    Preprints | 2014
    Carey A; Gesztesy F; Potapov D; Sukochev F; Tomilov Y, 2014, On the Witten index in terms of spectral shift functions, http://dx.doi.org/10.48550/arxiv.1404.0740
    Preprints | 2013
    Caspers M; Potapov D; Sukochev F; Zanin D, 2013, Weak type estimates for the absolute value mapping, http://dx.doi.org/10.48550/arxiv.1309.3378
    Preprints | 2012
    Caspers M; Montgomery-Smith S; Potapov D; Sukochev F, 2012, The best constants for operator Lipschitz functions on Schatten classes, http://dx.doi.org/10.48550/arxiv.1209.3948
    Preprints | 2012
    Kalton N; Lord S; Potapov D; Sukochev F, 2012, Traces of compact operators and the noncommutative residue, http://dx.doi.org/10.48550/arxiv.1210.3423
    Preprints | 2012
    Potapov D; Skripka A; Sukochev F, 2012, Higher order spectral shift for contractions, http://dx.doi.org/10.48550/arxiv.1210.8227
    Preprints | 2011
    Caspers M; Potapov D; Sukochev F, 2011, The Walsh basis in the Lp-spaces of hyperfinite III_\lambda-factors, 0 < \lambda <= 1, http://dx.doi.org/10.48550/arxiv.1111.2403
    Preprints | 2010
    Aleksandrov A; Peller V; Potapov D; Sukochev F, 2010, Functions of normal operators under perturbations, http://dx.doi.org/10.48550/arxiv.1008.1638
    Preprints | 2010
    Aleksandrov A; Peller V; Potapov D; Sukochev F, 2010, Functions of perturbed normal operators, http://dx.doi.org/10.48550/arxiv.1003.5286
    Preprints | 2009
    Potapov D; Skripka A; Sukochev F, 2009, Spectral shift function of higher order, http://dx.doi.org/10.48550/arxiv.0912.3056
    Preprints | 2008
    Carey A; Potapov D; Sukochev F, 2008, Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators, http://dx.doi.org/10.48550/arxiv.0807.2129
    Preprints | 2008
    Potapov D; Sukochev F, 2008, Non- (quantum) differentiable $C^1$-functions in the spaces with trivial Boyd indices, http://dx.doi.org/10.48550/arxiv.0808.2856
    Preprints | 2008
    Potapov D; Sukochev F, 2008, The Haar system in the preduals of hyperfinite factors, http://dx.doi.org/10.48550/arxiv.0808.2851
    Preprints | 2008
    Potapov D; Sukochev F, 2008, Unbounded Fredholm modules and double operator integrals, http://dx.doi.org/10.48550/arxiv.0808.2854
    Conference Papers | 2007
    Potapov D, 2007, 'Commutator estimates in the operator Lp-spaces', in Proceedings of the Centre for Mathematics and its applications, Centre for Mathematics and its applications, presented at Centre for Mathematics and its applications