Preprints and accepted papers
Linear formula for Operator Means, with Eduardo Ghiglioni, Juyoung Jeong and Yongdo Lim, preprint (2020), 20 pages.
Semigroups of operator means and generalized Karcher equations, preprint (2013), https://arxiv.org/abs/1208.5603, 76 pages.
Published papers
Ergodic theorems for the L1-Karcher mean, with Jorge Antezana, Eduardo Ghiglioni, Yongdo Lim, Acta Sci. Math. (Szeged) 90 (2024), pp. 575–591. https://doi.org/10.1007/s44146-024-00154-6
Convergence of semi-convex functions in CAT(1)-spaces, with Hedvig Gál, Calc. Var. PDE 63 (2024), 213. 10.1007/s00526-024-02823-4.
Strong law of large numbers for generalized operator means, with Zoltán Léka, Adv. Math. 457 (2024), 109933. https://doi.org/10.1016/j.aim.2024.109933. Warning! In Theorem 5.2 an extra assumption of local uniform integrability of (21) in x is missing, also in the proof of Theorem 5.2 we need an extra approximation step to effectively control the error terms using this uniform integrability. The rest of the paper, including section 6 is unaffected by this, since this uniform integrability is satisfied. An erratum will be written soon.
Approximation semigroups for resolvent maps, with B.J. Choi, U.C. Ji, Y. Lim, Banach J. Math. Anal. 18 (2024), 26, https://doi.org/10.1007/s43037-024-00336-y.
Analytic lifts of operator concave functions, Adv. Math. 408 (2022), 108583, https://doi.org/10.1016/j.aim.2022.108583
Existence, uniqueness and an ODE approach to the $L^1$-Karcher mean, with Yongdo Lim, Adv. Math. 376 (2021), 107435, https://doi.org/10.1016/j.aim.2020.107435.
The Karcher mean of linearly independent triples, with Eduardo Ghiglioni and Yongdo Lim, Linear Algebra and its Applications Volume 610 (2021), pp. 203-221.
A note on real operator monotone functions, with Marcell Gaál, International Mathematics Research Notices 2022:6 (2022), pp. 4259–4279.
Strong law of large numbers for the $L^1$-Karcher mean, with Yongdo Lim, Journal of Functional Analysis 279:7 (2020), 108672, https://doi.org/10.1016/j.jfa.2020.108672.
Loewner’s theorem in several variables, Journal of Mathematical Analysis and its Applications 490:1 (2020), 124233, https://doi.org/10.1016/j.jmaa.2020.124233.
Preface to the Proceedings of ILAS 2017: Connections, Twenty-first Conference of the International Linear Algebra Society, Iowa State University, 24-28 July 2017, with S. Guttel, L. Hogben and T. Stykel, Linear Algebra and its Applications 576 (2019), pp. 1-4.
Matrix-valued Jensen’s inequality and its application to eigenvalue analysis, with Yongdo Lim, (2018), Journal of Mathematical Analysis and its Applications, 464:2 (2018), pp. 1425-1440.
Gradient flows and a Trotter-Kato formula of semi-convex functions on CAT(1)-spaces, with Shin-ichi Ohta, Amer. J. Math. 139:4 (2017), pp. 937-965.
Operator means of probability measures and generalized Karcher equations, Advances in Mathematics 289 (2016), pp. 951-1007.
Discrete-time gradient flows and law of large numbers in Alexandrov spaces, with Shin-ichi Ohta, Calc. Var. PDE 54:2 (2015), pp. 1591-1610.
Weighted multivariable operator means of positive definite operators, with Dénes Petz, Linear Algebra and its Applications 463 (2014), pp. 134-153.
Weighted inductive means, with Yongdo Lim, Linear Algebra and its Applications 453 (2014), pp. 59-83.
Weighted deterministic walks for the least squares mean on Hadamard spaces, with Yongdo Lim, Bull. of the London Math. Soc. 46:3 (2014), pp. 561-570.
Approximations to the Karcher mean on Hadamard spaces via geometric power means, with Yongdo Lim, Forum. Math. 27:5 (2015), pp. 2609-2635.
Matrix power means and the Karcher mean, with Yongdo Lim, Journal of Functional Analysis 262:4 (2012), pp. 1498-1514.
Weighted matrix means and symmetrization procedures, Linear Algebra and its Applications 438:4 (2013) pp. 1746-1768.
Means in metric spaces and the center of mass, Journal of Mathematical Analysis and its Applications 381 (2011), pp. 383-391.
A multivariable extension of two-variable matrix means, SIAM Journal on Matrix Analysis and its Applications 32:2 (2011), pp. 385-393.
The Riemann Barycenter Computation and Means of Several Matrices, International Journal of Computational and Mathematical Sciences, 3(3) (2009), pp. 128-133.
On professor Tsuyoshi Ando (Tsuyoshi Ando professzorról), with Dénes Petz, Polygon, vol. XVI, no. 1 (2007), pp. 9-16.
Thesis
PhD thesis: Matrix means and geometric constructions, (2012), 127pp, Adviser: prof. István Vajk.
MSc thesis: On Affne matrix means, (2011), 60pp, Adviser: prof. Pál Hegedűs.
Other Publications and Conference Proceedings
Deterministic walks and quasi-subgradient methods for the Karcher mean on NPC spaces, Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013, Proceedings, Springer-Verlag Berlin and Heidelberg GmbH & Co. K (2013), pp. 802-809.
Operator means as unique solutions of operator equations, Research on structures of operators via methods in geometry and probability theory, Kyoto RIMS Kôkyûroku, No. 1839 (2013), pp. 67-81.
Geometric means, Proceedings of the Automation and Applied Computer Science Workshop (AACS 2010), pp. 267-274.
An iterative approach to means of matrices, Proceedings of the Automation and Applied Computer Science Workshop (AACS 2009), pp. 271-284, ISBN: 978-963-420-978-2.
The Riemann Barycenter Computation and Means of Several Matrices, Proceedings of World Academy of Science, Engineering and Technology, Vol. 30, July 2008, ISSN: 1307-6884, pp. 60-66.
Matrix Means and the Riemannian Center of Mass, Proceedings of the Automation and Applied Computer Science Workshop (AACS 2008), pp. 35-49, ISBN 978-963-420-955-3.
On means of several positive matrices and numbers, Proceedings of the Automation and Applied Computer Science Workshop (AACS 2007), pp. 283-291, ISBN 978-963-420-909-6.
Direct Rendering of B-spline Surfaces, Proceedings of the Automation and Applied Computer Science Workshop (AACS 2007), pp. 307-313, ISBN 978-963-420-909-6.
If all fails, you can always fall back on Ms. Elk’s Brontosaurus theory.
Miklós Pálfia 