Main Publications

Submitted

• E. E. Berdysheva, N. Dyn, E. Farkhi, A. Mokhov, The pointwise limit of metric integral operators approximating set-valued functions, submitted.

Peer-Reviewed Publications

• E. E. Berdysheva, N. Dyn, E. Farkhi, A. Mokhov, Metric approximation of set-valued functions of bounded variation by integral operators, Constructive Approximation (2024), published online.

• E. E. Berdysheva and Sz. Gy. Révész, Delsarte’s extremal problem and packing on locally compact Abelian groups, Annali della Scuola Normale di Pisa – Classe di Scienze (5), XXIV (2023), 1007–1052.

• E. E. Berdysheva, N. Dyn, E. Farkhi, A. Mokhov, Metric Fourier approximation of set-valued functions of bounded variation, J. Fourier Anal. Appl. 27 (2021), Article 17, 38 pages.

• E. E. Berdysheva, S. N. Mekhmonzoda, M. Sh. Shabozov, Approximation of functions of several variables by continuous linear splines on rectilinear grids, Jaen Journal on Approximation 12 (2021), 1–23.

• E. E. Berdysheva, K. Hennings, M. Heilmann, Pointwise convergence of Bernstein-Durrmeyer type operators with respect to a collection of measures, J. Approx. Theory 251 (2020), Article 105339, 12 pages.

• E. E. Berdysheva, N. Dyn, E. Farkhi, A. Mokhov, Metric approximation of set-valued functions of bounded variation, J. Comput. Appl. Math. 349 (2019), 251–264.

• E. E. Berdysheva and M. A. Filatova, On the best approximation of the infinitesimal generator of a contraction semigroup in a Hilbert space, Ural Mathematical Journal 3(2) (2017), 40–45.

• E. E. Berdysheva and E. Al-Aidarous, Szász-Mirakjan-Durrmeyer and Baskakov-Durrmeyer operators with respect to arbitrary measure, Jaen Journal on Approximation 8(1) (2016), 1–26.

• E. E. Berdysheva, Operators of Durrmeyer type with respect to arbitrary measure, In: Mathematical Analysis and its Applications (P. N. Agrawal, R. N. Mohapatra, U. Singh, H. M. Srivastava, Eds.), Springer Proceedings in Mathematics & Statistics, Springer (2015), 255–263.

• E. E. Berdysheva and H. Berens, On a discrete Turán problem for ℓ-1 radial functions, Chapter 19, In: New Perspectives on Approximation and Sampling Theory – Festschrift in honor of Paul Butzer’s 85th birthday (G. Schmeisser and A. Zayed, Eds.), Applied and Numerical Harmonic Analysis, Birkhaeuser (2014), 447–468.

• E. E. Berdysheva and B.-Z. Li, On L^p-convergence of Bernstein-Durrmeyer operators with respect to arbitrary measure, Publ. Inst. Math., Nouv. Sér. 96(110) (2014), 23–29.

• E. E. Berdysheva, Bernstein-Durrmeyer operators with respect to arbitrary measure, II: pointwise convergence, J. Math. Anal. Appl. 418 (2014), 734–752.

• E. E. Berdysheva, Uniform convergence of Bernstein-Durrmeyer operators with respect to arbitrary measure, J. Math. Anal. Appl. 394 (2012), 324–336.

• E. E. Berdysheva and K. Jetter, Multivariate Bernstein-Durrmeyer operators with arbitrary weight functions, J. Approx. Theory 162 (2010), 576–598.

• U. Abel and E. E. Berdysheva, Complete asymptotic expansion for multivariate Bernstein-Durrmeyer operators and quasi-interpolants, J. Approx. Theory 162 (2010), 201–220.

• E. E. Berdysheva and H. Berens, Über ein Turansches Problem für ℓ-1 radiale, positiv definite Funktionen, II, J. Approx. Theory 160 (2009), 71–88.

• E. E. Berdysheva, Studying Baskakov-Durrmeyer operators and quasi-interpolants via special functions, J. Approx. Theory 149 (2007), 131–150.

• E. Berdysheva, K. Jetter, J. Stöckler, Durrmeyer operators and their natural quasi-interpolants, In: Topics in Multivariate Approximation and Interpolation (K. Jetter et al., Eds.), Elsevier (2006), 1–21.

• E. E. Berdysheva and H. Berens, Über ein Turansches Problem für ℓ-1 radiale, positiv definite Funktionen, Result. Math. 47 (2005), 17–32.

• E. Berdysheva, K. Jetter, and J. Stöckler, Bernstein-Durrmeyer type quasi-interpolants on intervals, In: Approximation Theory (D. K. Dimitrov, G. Nikolov, and R. Uluchev, Eds.), Marin Drinov Acad. Publ. House, Sofia (2004), 32–42.

• E. Berdysheva, K. Jetter, J. Stöckler, New polynomial preserving operators on simplices: direct results, J. Approx. Theory 131 (2004), 59–73.

• E. E. Berdysheva, Optimal set of the modulus of continuity in the sharp Jackson inequality in the space L₂, Mat. Zametki 76(5) (2004), 666–674 (in Russian); English transl.: Math. Notes 76(5) (2004), 620–627.

• V. V. Arestov, E. E. Berdysheva, H. Berens, On pointwise Turán's problem for positive definite functions, East J. Approx. 9(1) (2003), 31–42.

• V. V. Arestov and E. E. Berdysheva, The Turán problem for a class of polytopes, East J. Approx. 8(3) (2002), 381–388.

• V. V. Arestov and E. E. Berdysheva, Turán's problem for positive definite functions with supports in a hexagon, Proceedings of the Steklov Institute of Mathematics, Suppl. 1 (2001), S20–S29. Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, V.7, N 1 (2001).

• E. E. Berdysheva, Several related extremal problems for multivariate entire functions of exponential type, East J. Approx. 6(2) (2000), 241–260.

• E. E. Berdysheva, Two related extremal problems for entire functions of several variables, Mat. Zametki 66, 3 (1999), 336–350 (in Russian); English transl.: Math. Notes 66 (1999), 271–282.

• E. E. Berdysheva, An extremal problem for entire functions of exponential type with nonnegative mean value, East J. Approx. 3(4) (1997), 393–402.

• E. E. Berdysheva, On the best approximation of the differentiation operator in L₂(0, ∞), East J. Approx. 2(3) (1996), 281–287.