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Keywords: submatrix, operator norm, sampling discretization.

### Research Interests:

→ The restriction of operators to subspaces;

→ Sampling discretization of the norm.

### Publications (recent):

*2023*

→ I. V. Limonova, "Dense weakly lacunary subsystems in orthogonal systems and the maximal partial sum operator", Mat. Sb., 214:11 (2023), 63–88, DOI.

*2022*

→ I. V. Limonova, "On the existence of dense subsystems with lacunarity property in orthogonal systems", Uspekhi Mat. Nauk, 77:5(467) (2022), 191–192, DOI.

→ B. Kashin, E. Kosov, I. Limonova, V. Temlyakov, "Sampling discretization and related problems", Journal of Complexity, 71(2022), 101653-55, DOI, arXiv.

→ I. Limonova, V. N. Temlyakov, "On sampling discretization in \(L_2\)", J. Math. Anal. Appl., 515:2 (2022), 126457, DOI, arXiv.

*2021*

→ I. V. Limonova, "On exact discretization of the \(L_2\)-norm with a negative weight", Math. Notes, 110:3 (2021), 458–462, DOI, arXiv.

*2020*

→ I. V. Limonova, "Decomposing a Matrix into Two Submatrices with Extremely Small Operator Norm", Math. Notes, 108:1 (2020), 137–141, DOI, arXiv.

→ B. S. Kashin, I. V. Limonova, "Weakly Lacunary Orthogonal Systems and Properties of the Maximal Partial Sum Operator for Subsystems", Proc. Steklov Inst. Math., 311 (2020), 152–170, DOI.

*2019*

→ B. S. Kashin, I. V. Limonova, "Decomposing a Matrix into two Submatrices with Extremally Small (2,1)-Norm", Math. Notes, 106:1 (2019), 63–70, DOI.

→ B. S. Kashin, I. V. Limonova, "Selecting a dense weakly lacunary subsystem in a bounded orthonormal system", Russian Math. Surveys, 74:5 (2019), 956–958, DOI.

*2016*

→ I. V. Limonova, "Decomposing a matrix into two submatrices with smaller (2,1)-Norm", Russian Math. Surveys, 71:4 (2016), 781–783, DOI.