→ USC, Dept. of Mathematics, Professor, Carolina Distinguished Professor

→ Lomonosov Moscow State University, Lead Scientist

→ Steklov Institute of Mathematics (RAS), Lead Scientist

E-mail:

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Keywords: approximation theory, greedy approximations, dictionaries, discretization, compressed sensing, Lebesgue-type inequalities, n-widths, integral operators, discrepancy, incoherent systems.

Education:

→ Dr. Hab., Steklov Institute of Mathematics, 1981;

→ Ph.D., Steklov Institute of Mathematics, 1978.

### Research Interests:

→ Greedy approximation: with respect to bases and to redundant systems (dictionaries), Lebesgue-type inequalities.

→ Compressed sensing: exact and approximate recovery by \(l_1\)-minimization and greedy methods.

→ Incoherent systems. Compressed sensing in Banach spaces.

→ Learning theory: mathematical aspects of supervised learning. Application of approximation theory and greedy approximation in regression and classification problems.

→ Numerical integration: multivariate case, discrepancy theory, Fibonacci cubature formulas, sparse grids.

### Honors and Awards:

→ USC Educational Foundation Award for Research in Science, Mathematics and Engineering, 2003.

→ Invited Hour Speaker, Foundations of Computational Mathematics, Santander, Spain, July 8, 2005.

→ Invited Hour Speaker, Curves and Surfaces, Avignon, France, June 29, 2006.

→ Invited forty-five minutes lecture in the section Analysis of the International Congress of Mathematicians, Madrid, Spain, August 2006.

→ Carolina Distinguished Professor, August 15, 2007.

### Publications (recent):

*2024*

→ V. N. Temlyakov, "Sparse sampling recovery in integral norms on some function classes", Mat. Sb., 215:10 (2024), 146–166, DOI.

→ I. V. Limonova, Yu. V. Malykhin, V. N. Temlyakov, "One-sided discretization inequalities and recovery from samples", Uspekhi Mat. Nauk, 79:3 (477) (2024), 149–180, DOI.

→ V. N. Temlyakov, "Rate of convergence of Thresholding Greedy Algorithms", Mat. Sb., 215:2 (2024), 147–162, DOI.

→ F. Dai, V. Temlyakov, "Random points are good for universal discretization", Journal of Mathematical Analysis and Applications, 529:1 (2024), 127570–28, DOI.

→ E. Kosov, V. Temlyakov, "Sampling discretization of the uniform norm and applications", J. Math. Anal. Appl., 538:2 (2024), 128431, DOI, arXiv.

*2023*

→ B. Kashin, S. Konyagin, V. Temlyakov, "Sampling discretization of the uniform norm", Constr. Approx., 57 (2023), 663–694, DOI, arXiv.

→ F. Dai, A. Prymak, A. Shadrin, V.N. Temlyakov, S. Tikhonov, "On the cardinality of lower sets and universal discretization", Journal of Complexity, 76 (2023), 101726, DOI.

→ F. Dai, E. Kosov, V. Temlyakov, "Some improved bounds in sampling discretization of integral norms", Journal of Functional Analysis, 2023, 109951, DOI.

→ V. Temlyakov, "Sampling discretization error of integral norms for function classes with small smoothness", Journal of Approximation Theory, 293 (2023), 105913, DOI.

→ V. Temlyakov, F. Dai, "Universal Sampling Discretization", Constructive Approximation, 2023, 1–25, DOI.

→ V. Temlyakov, "On universal sampling representation", Pure and Applied Functional Analysis, 8:2 (2023), 627–645, arXiv.

→ V. Temlyakov, "On the Rate of Convergence of Greedy Algorithms", Mathematics, 11:11 (2023), 2559, DOI.

*2022*

→ V. Temlyakov, "A remark on entropy numbers", Studia Mathematica, 263:2 (2022), 199–208, DOI, arXiv.

→ V. N. Temlyakov, "Numerical Integration and Discrepancy Under Smoothness Assumption and Without It", Constr. Approx. 55 (2022), 743–771, DOI, arXiv.

→ F. Dai, V. Temlyakov, "Sampling discretization of integral norms and its application", Approximation Theory, Functional Analysis, and Applications. Collected papers. On the occasion of the 70th birthday of Academician B. S. Kashin. Trudy MIAN, 319 (2022), 106–119, arXiv.

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

→ T. Ullrich, V. N. Temlyakov, "Approximation of functions with small mixed smoothness in the uniform norm", Journal of Approximation Theory, 277 (2022), 105718, DOI, arXiv.

→ A. Dereventsov, V. N. Temlyakov, "Biorthogonal greedy algorithms in convex optimization", Appl. Comput. Harmon. Anal., 60 (2022), 489–511, DOI, arXiv.

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

*2021*

→ T. Ullrich, V.N. Temlyakov, "Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness", J. Complexity, 67 (2021), 101575, DOI, arXiv.

→ F. Dai, A. Prymak, A. Shadrin, S. Tikhonov, V.N. Temlyakov, "Entropy numbers and Marcinkiewicz-type discretization theorems", J. Funct. Anal., 281:6 (2021), 109090, DOI, arXiv.

→ A.S. Rubtsova, K.S. Ryutin, V.N. Temlyakov, "On the fixed volume discrepancy of the Korobov point sets", Sb. Math., 212:8 (2021), 1180–1192, DOI, arXiv.

→ F. Dai, A. Prymak, A. Shadrin, S. Tikhonov, V. N. Temlyakov, "Sampling discretization of integral norms", Constr. Approx. (2021), DOI, arXiv.

→ V. N. Temlyakov, "Sampling discretization of integral norms of the hyperbolic cross polynomials", Function spaces, approximation theory, and related problems of analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, DOI, arXiv.

→ S. Dilworth, G. Garrigós, E. Hernández, D. Kutzarova, V. Temlyakov, "Lebesgue-type inequalities in greedy approximation", J. Funct. Anal., 280 (2021), 108885, DOI, arXiv.

→ V. N. Temlyakov, "On optimal recovery in \(L_2\)", J. Complexity, 65 (2021), DOI, arXiv.

*2020*

→ V. N. Temlyakov, M. Ullrich, "On the fixed volume discrepancy of the Fibonacci sets in the integral norms", J. Complexity, 61 (2020), 101472, DOI, arXiv.

→ L. Burusheva, V. Temlyakov, "Sparse approximation of individual functions", J. Approx. Theory, 259 (2020), 105471, DOI, arXiv.

→ V.N. Temlyakov, "Fixed volume discrepancy in the periodic case", Proceedings of the International Conference in Approximation Theory, May 2017, Georgia, USA: Topics in Classical and Modern Analysis, Birkhäuser, 2019, 315–330, DOI, arXiv.

*2019*

→ V. N. Temlyakov, "Smooth fixed volume discrepancy, dispersion, and related problems", J. Approx. Theory, 237 (2019), 113–134, DOI.

→ F. Dai, A. Prymak, V. N. Temlyakov, S. Yu. Tikhonov, "Integral norm discretization and related problems", Russian Math. Surveys, 74:4 (2019), 579–630, DOI, arXiv.

→ A. V. Dereventsov, V. N. Temlyakov, "A unified way of analyzing some greedy algorithms", J. Funct. Anal., 277:12 (2019), 108286–30, DOI, arXiv.

→ V.N. Temlyakov, "Sampling discretization error of integral norms for function classes." Journal of Complexity 54 (2019): 101408, DOI.

*2018*

→ V.N. Temlyakov, "Universal discretization", J. Complexity, 47 (2018), 97–109, DOI, arXiv.

→ V. N. Temlyakov, "The Marcinkiewicz–type discretization theorems", Constr. Approx., 48:2 (2018), 337–369, DOI, arXiv.

→ B. S. Kashin, V. N. Temlyakov, "Observations on discretization of trigonometric polynomials with given spectrum", Russian Math. Surveys, 73:6 (2018), 1128–113, DOI, PDF.

→ S. J. Dilworth, D. Kutzarova, V. N. Temlyakov, B. Wallis, "Weight-almost greedy bases", Proc. Steklov Inst. Math., 303 (2018), 109–128, DOI, PDF.

→ V.N. Temlyakov, "Connections between numerical integration, discrepancy, dispersion, and universal discretization", SMAI Journal of Computational Mathematics, 5 (2019), 185–209, DOI, arXiv.

*2017*

→ V. Temlyakov, "On the entropy numbers of the mixed smoothness function classes", J. Approx. Theory, 217 (2017), 26–56, DOI, arXiv.

→ V. Temlyakov, "Constructive Sparse Trigonometric Approximation for Functions with Small Mixed Smoothness", Constr. Approx., 45 (2017), 467–495, DOI, arXiv.

→ V. Temlyakov, S. Tikhonov, "Remez-Type and Nikol’skii-Type Inequalities: General Relations and the Hyperbolic Cross Polynomials", Constr. Approx., 46:3 (2017), 593–615, DOI.

→ V.N. Temlyakov, "The Marcinkiewicz-type discretization theorems for the hyperbolic cross polynomials", Jaen Journal on Approximation, 9:1(2017), 37–63, arXiv.