Kachurovskii, A. G.; Podvigin, I. V.; Todikov, V. È.; Khakimbaev, A. Zh. A spectral criterion for power-law convergence rate in the ergodic theorem for \({ \mathbb{Z} }^d\) and \({ \mathbb{R} }^d\) actions. (English. Russian original) Zbl 07804694 Sib. Math. J. 65, No. 1, 76-95 (2024); translation from Sib. Mat. Zh. 65, No. 1, 92-114 (2024). Reviewer: Thomas B. Ward (Durham) MSC: 37A30 37B05 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} et al., Sib. Math. J. 65, No. 1, 76--95 (2024; Zbl 07804694); translation from Sib. Mat. Zh. 65, No. 1, 92--114 (2024) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V.; Khakimbaev, A. Zh. Uniform convergence on subspaces in the von Neumann ergodic theorem with discrete time. (English. Russian original) Zbl 1523.37012 Math. Notes 113, No. 5, 680-693 (2023); translation from Mat. Zametki 113, No. 5, 713-730 (2023). Reviewer: Hasan Akin (Şanlıurfa) MSC: 37A30 37A05 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} et al., Math. Notes 113, No. 5, 680--693 (2023; Zbl 1523.37012); translation from Mat. Zametki 113, No. 5, 713--730 (2023) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V.; Todikov, V. E. Uniform convergence on subspaces in von Neumann’s ergodic theorem with continuous time. arXiv:2302.13586 Preprint, arXiv:2302.13586 [math.DS] (2023). MSC: 37A30 37A10 47A35 60G10 BibTeX Cite \textit{A. G. Kachurovskii} et al., ``Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time'', Preprint, arXiv:2302.13586 [math.DS] (2023) Full Text: arXiv OA License
Kachurovskii, A. G.; Podvigin, I. V.; Svishchev, A. A. The maximum pointwise rate of convergence in Birkhoff’s ergodic theorem. (English. Russian original) Zbl 1471.37005 J. Math. Sci., New York 255, No. 2, 119-123 (2021); translation from Zap. Nauchn. Semin. POMI 498, 18-25 (2020). Reviewer: Piotr Garbaczewski (Opole) MSC: 37A30 37A10 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} et al., J. Math. Sci., New York 255, No. 2, 119--123 (2021; Zbl 1471.37005); translation from Zap. Nauchn. Semin. POMI 498, 18--25 (2020) Full Text: DOI
Kachurovskii, Alexander; Podvigin, Ivan To recovering of continuous function by its sequences of Fejér sums at given set of points. (English) Zbl 1467.42004 Proc. Int. Geom. Cent. 13, No. 3, 1-9 (2020). MSC: 42A16 40G05 PDFBibTeX XMLCite \textit{A. Kachurovskii} and \textit{I. Podvigin}, Proc. Int. Geom. Cent. 13, No. 3, 1--9 (2020; Zbl 1467.42004) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Measuring the rate of convergence in the Birkhoff ergodic theorem. (English. Russian original) Zbl 1427.37004 Math. Notes 106, No. 1, 52-62 (2019); translation from Mat. Zametki 106, No. 1, 40-52 (2019). MSC: 37A30 37A05 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Math. Notes 106, No. 1, 52--62 (2019; Zbl 1427.37004); translation from Mat. Zametki 106, No. 1, 40--52 (2019) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Fejér sums and Fourier coefficients of periodic measures. (English. Russian original) Zbl 1403.37016 Dokl. Math. 98, No. 2, 464-467 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 482, No. 4, 381-384 (2018). MSC: 37A45 42A16 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 98, No. 2, 464--467 (2018; Zbl 1403.37016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 482, No. 4, 381--384 (2018) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Fejér sums for periodic measures and the von Neumann ergodic theorem. (English. Russian original) Zbl 1400.37009 Dokl. Math. 98, No. 1, 344-347 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 481, No. 4, 358-361 (2018). MSC: 37A30 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 98, No. 1, 344--347 (2018; Zbl 1400.37009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 481, No. 4, 358--361 (2018) Full Text: DOI
Kachurovskiĭ, A. G.; Podvigin, I. V. Large deviations of the ergodic averages: from Hölder continuity to continuity almost everywhere. (Russian, English) Zbl 1399.37001 Mat. Tr. 20, No. 1, 97-120 (2017); translation in Sib. Adv. Math. 28, No. 1, 23-38 (2018). MSC: 37A30 37A60 60F10 PDFBibTeX XMLCite \textit{A. G. Kachurovskiĭ} and \textit{I. V. Podvigin}, Mat. Tr. 20, No. 1, 97--120 (2017; Zbl 1399.37001); translation in Sib. Adv. Math. 28, No. 1, 23--38 (2018) Full Text: DOI
Kachurovskii, Aleksandr G.; Podvigin, Ivan V. Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems. (English. Russian original) Zbl 1370.37014 Trans. Mosc. Math. Soc. 2016, 1-53 (2016); translation from Tr. Mosk. Mat. O.-va 77, No. 1, 1-66 (2016). Reviewer: Alejandro Mesón (La Plata) MSC: 37A30 37D20 37D50 60G10 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Trans. Mosc. Math. Soc. 2016, 1--53 (2016; Zbl 1370.37014); translation from Tr. Mosk. Mat. O.-va 77, No. 1, 1--66 (2016) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Large deviations and rates of convergence in the Birkhoff ergodic theorem: from Hölder continuity to continuity. (English. Russian original) Zbl 1362.37014 Dokl. Math. 93, No. 1, 6-8 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 1, 12-15 (2016). MSC: 37A30 37A50 37A60 60F10 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 93, No. 1, 6--8 (2016; Zbl 1362.37014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 1, 12--15 (2016) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Correlations, large deviations, and rates of convergence in ergodic theorems for characteristic functions. (English. Russian original) Zbl 1333.60041 Dokl. Math. 91, No. 2, 204-207 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 461, No. 5, 509-512 (2015). Reviewer: Thorsten Dickhaus (Berlin) MSC: 60F10 60F99 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 91, No. 2, 204--207 (2015; Zbl 1333.60041); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 461, No. 5, 509--512 (2015) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Rate of convergence in ergodic theorems for the planar periodic Lorentz gas. (English. Russian original) Zbl 1352.37012 Dokl. Math. 89, No. 2, 139-142 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 455, No. 1, 11-14 (2014). MSC: 37A30 47A35 60F10 37A05 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 89, No. 2, 139--142 (2014; Zbl 1352.37012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 455, No. 1, 11--14 (2014) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Large deviations and the rate of convergence in the Birkhoff ergodic theorem. (English. Russian original) Zbl 1370.37012 Math. Notes 94, No. 4, 524-531 (2013); translation from Mat. Zametki 94, No. 4, 569-577 (2013). Reviewer: Chryssoula Ganatsiou (Larissa) MSC: 37A30 28E05 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Math. Notes 94, No. 4, 524--531 (2013; Zbl 1370.37012); translation from Mat. Zametki 94, No. 4, 569--577 (2013) Full Text: DOI
Kachurovskii, A. G.; Podvigin, I. V. Rates of convergence in ergodic theorems for certain billiards and Anosov diffeomorphisms. (English. Russian original) Zbl 1328.37005 Dokl. Math. 88, No. 1, 385-387 (2013); translation from Dokl. Akad. Nauk, 451, No. 1, 11-13 (2013). Reviewer: David Ralston (Westbury) MSC: 37A30 37D20 37A25 PDFBibTeX XMLCite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 88, No. 1, 385--387 (2013; Zbl 1328.37005); translation from Dokl. Akad. Nauk, 451, No. 1, 11--13 (2013) Full Text: DOI