Select Publications
Book Chapters
, 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, 'The Witten index and the spectral shift function', Reviews in Mathematical Physics, 34, http://dx.doi.org/10.1142/S0129055X22500118
, 2019, 'On a Trace Formula for Functions of Noncommuting Operators', Mathematical Notes, 106, pp. 481 - 487, http://dx.doi.org/10.1134/S0001434619090189
, 2019, 'WEAK TYPE COMMUTATOR AND LIPSCHITZ ESTIMATES: RESOLUTION OF THE NAZAROV-PELLER CONJECTURE', AMERICAN JOURNAL OF MATHEMATICS, 141, pp. 593 - 610, http://dx.doi.org/10.1353/ajm.2019.0019
, 2019, 'FrÉchet differentiability of the norm of L
, 2019, 'О формуле следов для функций от некоммутирующих операторов', Matematicheskie Zametki, 106, pp. 483 - 490, http://dx.doi.org/10.4213/mzm12259
, 2018, 'On the Global Limiting Absorption Principle for Massless Dirac Operators', Annales Henri Poincare, 19, pp. 1993 - 2019, http://dx.doi.org/10.1007/s00023-018-0675-5
, 2017, 'Multilinear Schur multipliers and Schatten properties of operator Taylor remainders', Advances in Mathematics, 320, pp. 1063 - 1098, http://dx.doi.org/10.1016/j.aim.2017.09.012
, 2017, 'On the Witten index in terms of spectral shift functions', Journal d'Analyse Mathematique, 132, pp. 1 - 61, http://dx.doi.org/10.1007/s11854-017-0003-x
, 2016, 'Trace formulas for a class of non-Fredholm operators: A review', Reviews in Mathematical Physics, 28, http://dx.doi.org/10.1142/S0129055X16300028
, 2016, 'Peller's problem concerning Koplienko–Neidhardt trace formulae: the unitary case', Journal of Functional Analysis, 271, pp. 1747 - 1763, http://dx.doi.org/10.1016/j.jfa.2016.05.015
, 2016, 'Resolution of Peller's problem concerning Koplienko-Neidhardt trace formulae', Proceedings of the London Mathematical Society, 113, pp. 113 - 139, http://dx.doi.org/10.1112/plms/pdw024
, 2016, 'On index theory for non-Fredholm operators: A (1 + 1)-dimensional example', Mathematische Nachrichten, 289, pp. 575 - 609, http://dx.doi.org/10.1002/mana.201500065
, 2016, 'Functions of unitary operators: Derivatives and trace formulas', Journal of Functional Analysis, 270, pp. 2048 - 2072, http://dx.doi.org/10.1016/j.jfa.2016.01.001
, 2016, 'Double operator integral methods applied to continuity of spectral shift functions', Journal of Spectral Theory, 6, pp. 747 - 779, http://dx.doi.org/10.4171/JST/140
, 2015, 'Singular traces and perturbation formulae of higher order', Journal of Functional Analysis, 269, pp. 1441 - 1481, http://dx.doi.org/10.1016/j.jfa.2015.04.019
, 2015, 'Trace formulas for resolvent comparable operators', Advances in Mathematics, 272, pp. 630 - 651, http://dx.doi.org/10.1016/j.aim.2014.12.016
, 2015, 'On the Arazy conjecture concerning Schur multipliers on Schatten ideals', Advances in Mathematics, 268, pp. 404 - 422, http://dx.doi.org/10.1016/j.aim.2014.09.021
, 2015, 'Weak type estimates for the absolute value mapping', Journal of Operator Theory, 73, pp. 361 - 384, http://dx.doi.org/10.7900/jot.2013dec20.2021
, 2014, 'The best constants for operator Lipschitz functions on Schatten classes', Journal of Functional Analysis, 267, pp. 3557 - 3579, http://dx.doi.org/10.1016/j.jfa.2014.08.018
, 2014, 'Fréchet differentiability of Sp norms', Advances in Mathematics, 262, pp. 436 - 475, http://dx.doi.org/10.1016/j.aim.2014.05.011
, 2014, 'Higher-order spectral shift for contractions', Proceedings of the London Mathematical Society, 108, pp. 327 - 349, http://dx.doi.org/10.1112/plms/pdt024
, 2014, 'Functions of unitary operators: Derivatives and trace formulas', Journal of Functional Analysis, http://dx.doi.org/10.1016/j.jfa.2016.01.001
, 2014, 'A Jost-Pais-Type Reduction of Fredholm Determinants and Some Applications', Integral Equations and Operator Theory, 79, pp. 389 - 447, http://dx.doi.org/10.1007/s00020-014-2150-0
, 2014, 'Fréchet differentiability of the norm of L
, 2014, 'Krein's trace theorem revisited', Journal of Spectral Theory, 4, pp. 415 - 430, http://dx.doi.org/10.4171/JST/75
, 2013, 'Spectral shift function of higher order', Inventiones Mathematicae, 193, pp. 501 - 538, http://dx.doi.org/10.1007/s00222-012-0431-2
, 2013, 'On Hilbert-Schmidt compatibility', Operators and Matrices, 7, pp. 1 - 33, http://dx.doi.org/10.7153/oam-07-01
, 2013, 'The Walsh basis in the Lp-spaces of hyperfinite IIIλ factors, 0', Journal of Mathematical Analysis and Applications, 408, pp. 154 - 164, http://dx.doi.org/10.1016/j.jmaa.2013.06.003
, 2013, 'Traces of compact operators and the noncommutative residue', Advances in Mathematics, 235, pp. 1 - 55, http://dx.doi.org/10.1016/j.aim.2012.11.007
, 2012, 'Koplienko Spectral Shift Function on the Unit Circle', Communications in Mathematical Physics, 309, pp. 693 - 702, http://dx.doi.org/10.1007/s00220-011-1338-2
, 2012, 'On the vector-valued Littlewood-Paley-Rubio de Francia inequality', Revista Matematica Iberoamericana, 28, pp. 839 - 856, http://dx.doi.org/10.4171/RMI/693
, 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, 105, pp. 661 - 702, http://dx.doi.org/10.1112/plms/pds014
, 2011, 'Functions of normal operators under perturbations', Advances in Mathematics, 226, pp. 5216 - 5251, http://dx.doi.org/10.1016/j.aim.2011.01.008
, 2011, 'Lipschitz functions, Schatten ideals, and unbounded derivations', Functional Analysis and Its Applications, 45, pp. 157 - 159
, 2011, 'Operator-Lipschitz functions in Schatten-von Neumann classes', ACTA Mathematica, 207, pp. 375 - 389, http://dx.doi.org/10.1007/s11511-012-0072-8
, 2011, 'Rosenthal inequalities in noncommutative symmetric spaces', Journal of Functional Analysis, 261, pp. 2890 - 2925, http://dx.doi.org/10.1016/j.jfa.2011.07.015
, 2011, 'The Haar system in the preduals of hyperfinite factors', Canadian Mathematical Bulletin, 54, pp. 347 - 363, http://dx.doi.org/10.4153/CMB-2011-007-7
, 2010, 'Double operator integrals and submajorization', Mathematical Modelling of Natural Phenomena (MMNP), 5, pp. 317 - 339, http://dx.doi.org/10.1051/mmnp/20105401
, 2010, 'Functions of perturbed normal operators', Comptes Rendus Mathematique, 348, pp. 553 - 558, http://dx.doi.org/10.1016/j.crma.2010.04.015
, 2010, 'Measures from Dixmier traces and zeta functions', Journal of Functional Analysis, 259, pp. 1915 - 1949, http://dx.doi.org/10.1016/j.jfa.2010.06.012
, 2009, 'Unbounded Fredholm modules and double operator integrals', Journal fur die Reine und Angewandte Mathematik, pp. 159 - 185, http://dx.doi.org/10.1515/CRELLE.2009.006
, 2009, 'Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators', Advances in Mathematics, 222, pp. 1809 - 1849
, 2009, 'Unbounded Fredholm modules and double operator integrals', Journal fur die Reine und Angewandte Mathematik, 626, pp. 159 - 185, http://dx.doi.org/10.15.15/CRELLE.2008
, 2008, 'Lipschitz and commutator estimates in symmetric operator spaces', Journal of Operator Theory, 59, pp. 211 - 234
, 2007, 'Non-(quantum) differentiable C1-functions in the spaces with trivial Boyd indices', Integral Equations and Operator Theory, 57, pp. 247 - 261
, 2006, 'Vector-valued multiplier theorems of Coifman-Rubio de Francia-Semmes type', Archiv der Mathematik, 87, pp. 245 - 254
, 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, 404, pp. 598 - 600
Conference Papers
, 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
Preprints
, 2021, The Witten index and the spectral shift function, , http://dx.doi.org/10.48550/arxiv.2101.06812