Books

  • Methods for Approximate Evaluation of Integrals (in Bulgarian), Nauka i Izkustvo, Sofia 1978, 209 pages.
  • Interpolation (in Bulgarian), Narodna Prosveta, Sofia 1984, 140 pages.
  • Theory of Spline Functions (in Bulgarian), Nauka i Izkustvo, Sofia 1990, 183 pages (with H. Hakopian).
  • Spline Functions and Multivariate Interpolations, Kluwer Academic Publishers, Dordrecht/Boston/London, 1993 (with H.Hakopian and A. Sahakian), 276 pages.
  • Lectures on Numerical Analysis (in Bulgarian), DARBA, Sofia 1995, 205 pages.

Editor

  • Optimal Recovery, Nova Science Publishers, New York, 1992 (with H. Wozniakowski).
  • Open Problems in Approximation Theory, CST Publishing, Singapore, 1994.
  • Approximation Theory: A volume dedicated to Blagovest Sendov, DARBA, Sofia, 2002, 410 pages.
  • Constructive Theory of Functions: Varna 2002, DARBA, Sofia, 2003, 452 pages.

Papers

  • On an estimation of the roots of algebraic equations. Zastosowania Matematyki XI, 2(1970), 195-205.
  • Supplement to the paper of Lupas and Müller. Aequationes Math. v.5, 1(1970), 38-39.
  • A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. R.S.Roumanie 14, 1(1970), 9-13 ( with .V. M. Veselinov ).
  • On a property of a class of linear positive operators. Annuaire Univ. Sofia, Fac. Math. v.64, 1971, 115-117 ( with Bl. Sendov ).
  • On the polynomials of best Hausdorff approximation (in Bulgarian). Annuaire Univ. Sofia, Fac. Math. v.64, 1971, 161-170.
  • Uniform parametric approximation of |x| by algebraic polynomials (in Bulgarian). Annuaire Univ. Sofia, Fac. Math. v.64, 1971, 331-337.
  • On the approximation of functions by Haar series. Mathematica 14, 2(1972), 189-192 (with V. M. Veselinov).
  • On the relation between the variation and the modulus of non-monotonisity of functions (in Bulgarian ). Izv. Mat. Inst. BAN v.13, 1972, 99-103.
  • On the approximation of functions by linear positive operators (in Bulgarian). Izv. Mat. Inst. BAN v.14 (1973), 179-187.
  • Optimal rate of integration and ε-entropy of a certain class of analytic functions (in Russian). Mat. Zametki 14, 1(1973), 3-10.
  • On the optimal method of integration of a certain class of analytic functions (in Russian).
    In: Proceedings of the II spring conference of the BMS, Vidin 1973. BAN, Sofia 1974, pp. 75-86.
  • On the ε-entropy of a class of analytic functions (in Russian). Annuaire Univ. Sofia, Fac. Math. v.66, 1974, 363-370
  • On an optimal quadrature formula. C. R. Acad. Bulg. Sci. 27, 5(1974), 619-621.
  • Optimal methods of interpolation in WrLq(M;a,b). C. R. Acad. Bulg. Sci. v.27, 7(1974), 885-888.
  • Best quadrature formulas for a certain class of analytic functions. Zastosowania Mat. XIV, 3(1974), 441-447.
  • New best quadrature formulas. C. R. Acad. Bulg. Sci. v.27, 12(1974), 1625-1627.
  • New best quadrature formulae. Serdica v.1, 1(1975), 110-120.
  • A note on the Wn∞ extremal problem of Favard. C. R. Acad. Bulg. Sci. 28, 9(1975), 1163-1165.
  • Optimal methods of integration in the class of differentiable functions. Zastosowania Mat. XV; 1(1975); 105-115.
  • Best methods of interpolation for certain classes of differentiable functions (in Russian). Mat. Zametki, v.17, 4(1975), 511-524.
  • Estimates for the ε-entropy of the space of functions, analytic in the unit disc (in Russian), Annuaire Univ. Sofia, Fac. Math. v.67, 1976, 191-194.
  • Favard's interpolation problem for periodic functions. Colloquia Mathematica Societatis Janos Boyai, 19. Fourier Analysis and Approximation Theory, Budapest (Hungary), 1976, 161-173.
  • A general method generating estimates for the best Hausdorff approximation. C. R. Acad. Bulg. Sci. v.29, 7(1976), 959-961 (with V. M. Veselinov).
  • Best cubature formulas. Serdica v.2, 1(1976), 42-52.
  • On an extremal problem (in Russian). Annuaire Univ. Sofia, Fac. Math. v.67, 1976, 195-203 (with M. Tzvetanov).
  • Numerical integration of functions with singularities (in Bulgarian). In: Proceedings of the III spring conference of the BMS, Burgas 1974, p. 120-123. BAN, Sofia 1976.
  • Best methods of integration with a weight of differentiable functions (in Russian). Dokladi AN ESSR v.25, 2(1976), 209-212.
  • Best methods of recovery of differentiable functions on the basis of their Fourier coefficients (in Russian). Serdica 2, 3(1976), 300-304.
  • Characterization and existence of optimal quadrature formulae for a class of differentiable functions (in Russian). Dokladi Akademii Nauk SSSR v. 232, 6(1977), 1233-1236.
  • A note on the optimal approximation of smooth periodic functions. C. R. Acad. Bulg. Sci. v.30, 6(1977), 809-812.
  • An optimal interpolation formula. J. Approximation Theory v.20, 3(1977), 264-274 (with V. G. Chernogorov).
  • Existence of extended monosplines of least deviation. C. R. Acad. Bulg. Sci. v.30, 7(1977), 985-988.
  • Existence of extended monosplines of least deviation. Serdica v.3, 3(1977), 261-272.
  • Best approximation of linear functionals in Wrp . PLISKA, Studia Mathematica Bulgarica v.1, 1977, 100-111.
  • Existence of optimal quadrature formulae with preassigned multiplicities of nodes. C. R. Acad. Bulg. Sci. v.30, 5(1977), 639-642.
  • Extremal problems in a set of polynomials with fixed multiplicities of zeros. C. R. Acad. Bulg. Sci. v.31, 4(1978), 377-380.
  • Existence and characterization of optimal quadrature formulas for certain class of differentiable functions. J. Approximation Theory v.22, 3(1978), 262-283.
  • Existence of optimal quadrature formulae with preassigned multiplicities of the nodes (in Russian). Mat. Sbornik 105(147), 3(1978), 342-370.
  • On certain convex problems in the theory of approximation (in Russian). Serdica v.5,1(1979), 83-96 (with V. M. Tihomirov).
  • Uniqueness of the optimal quadrature formulae (in Russian). Dokladi USSR, v.248, 2(1979), 272-274.
  • Uniqueness of the monosplines of least deviation. In: "Numerische Integration" (G. Hämmerlin, Ed.), ISNM 45, Birkhauser Verlag Basel, 1979, 67-97.
  • On the existence of optimal quadrature formulae for smooth functions. CALCOLO v.XVI, 1(1979), 61-70.
  • A generalization of Chebyshev polynomials. J. Approximation Theory v.26, 4(1979), 293-300.
  • Existence and characterization of monosplines of least Lp deviation. Proceeding of the International Conference on Constructive Functions Theory, Blagoevgrad 1977, Sofia, 1980, 249-268.
  • Perfect splines of least uniform deviation. Analysis Math. v.6, 3(1980), 185-193.
  • Uniqueness of optimal nodes of quadrature formulas. C. R. Acad. Bulg. Sci. v. 33, 2(1980), 167-169.
  • Uniqueness of the optimal nodes of quadrature formulae. Math. of Computation v.36, 154(1981), 525-546.
  • Proof of a conjecture of Erdös about the longest polynomial. Proceeding AMS, v.84, 1(1982), 99-103.
  • An extension of the Markov inequality. J. Approximation Theory v.35, 2(1982), 181-190.
  • Oscilating polynomials of least L1-norm. In: "Numerical Integration", G. Hämmerlin (Ed.), ISNM 57, Birkhäuser Verlag Basel, 1982, 25-33.
  • L1-approximation by Hermite interpolating polynomials with free nodes. C. R.Acad. Bulg. Sci. v.35, 8(1982), 1049-1051.
  • An extension of Markov's inequality (in Russian). Dokladi Akademii Nauk SSSR v.262,1(1982), 13-15.
  • A generalization of Chebyshev polynomials II. PLISKA, Studia mathematica bulgarica v.5, 1983, 93-96.
  • An extremal problem for polynomials. In: "Constructive Function Theory'81", Sofia, 1983, 229-233.
  • Sendov's conjecture about the critical points of polynoials, Fiz. mat. Spisanie, BAN, v. 26, 2(1984), 140-149 (in Bulgarian).
  • A note on the optimal quadrature in Hp. Numer. Math. 44, 1984, 301-308 (with J.-E. Anderson).
  • On a conjecture about critical points of a polynomial. ISNM 74, 1985, 83-93 (with Q. I. Rahman and J. Szynal).
  • On a conjecture of Sendov about the critical points of a polynomial. Math. Z. 190, 2(1985), 281-186 (with Q. I. Rahman and J. Szynal).
  • Generalized Gaussian quadrature formulas. J. Approximation Theory v.48, 4(1986), 335- 353 (with D. Braess and N. Dyn).
  • Comparison theorems in optimal recovery. In: "Optimal Algorithms" Bl. Sendov (Ed.), Sofia, BAN, 1986, 15-50.
  • L-approximations with constrains (in Russian). In: Proceedings of the International Conference on the Approximation of Functions, Kiev 1983, pp. 69-71. Nauka, Moscow 1987.
  • Periodic monosplines and perfect splines of least norm. Costractive Approximation 3(1987), 363-375 (with Daren Huang).
  • σ-Perfect splines and their application to optimal recovery problems. J. Complexity v.3, 1987, 429-450.
  • A note on the optimal recovery of functions in H1. J. Approximation Theory v.53, 1(1988), 67-77 (with G. Grozev).
  • B-splines with Birkhoff knots. Constructive Approximation 4(1988), 147-156.
  • Comparison of recovery schemes based on end-point values. Math. Balkanica, New Series, v.2, 1(1988), 11-17 (with Daren Huang).
  • On the optimal quadrature formulas in Wrq of quasi-Hermitian type. Approx. Theory and its Appl. v.4, 4(1988), 13-22 (with Daren Huang).
  • Generalized polynomials of minimal norm. J. Approximation Theory v.56, 1(1989), 91-100 (with R. B. Barrar and H. L. Loeb).
  • Comparison of optimal quadrature formulas. Numer. Math. 8(1990), 817-826 (with Daren Huang).
  • Optimal recovery of differentiable functions. Mat. Sbornik 181, 3(1990), 334-353 (In Russian).
  • Comparison of Birkhoff's type quadrature formulae. Math. Computaion 54(1990), 627-648(with G. Nikolov).
  • On the total positivity of the truncated power kernel. Colloq. Math. vol. LX/LXI (1990), 593-600.
  • Generalized Gaussian quadrature formulas for weak Tchebyshev systems. In: Optimal Recovery (B.Bojanov, H. Wozniakowski, Eds.), pp. 115-140, Nova Science, New York, 1992 (with G. Grozev and A. Zensykbaev)
  • An elementary proof of the Remez inequality. Amer. Math. Monthly v.100, 5(1993), 483-485.
  • Interpolation by periodic splines with Birkhoff knots. Numer. Math. 65(1993), 63-75.
  • Optimal recovery of functions and integrals. In: Proceedings of the First European Congress of Mathematics, Paris, July 6-10, 1992, Birkhäuser, Boston, 1994.
  • Polynomial inequalities. In: Open Problems in Approximation Theory (B. Bojanov, Ed.), 25-42, CST Publishing, Singapore, 1994.
  • Characterization of the smoothest interpolant. SIAM J. Math. Anal. , 25, No.6 (1994),1642-1655.
  • On certain extremal problems for polynomials. J. Math. Anal. Appl., 189(1995), 781-800 (with Q. I. Rahman).
  • An inequality of Duffin and Schaeffer type, East J. Approx. 1, 1(1995), 37-46.
  • Duffin and Schaeffer type inequality for ultraspherical polynomials, J. Approx. Theory, v. 84, 2(1996), 129-138 (with Geno Nikolov).
  • A Jackson type theorem for Tchebycheff systems, Math. Balkanica, v. 10, 1(1996), 73-82. 83.
  • On a polynomial inequality of Kolmogoroff's type, Proc. Amer. Math. Soc., 124, 2(1996), 491-496 (with A. K. Varma ).
  • Turan's inequality for trigonometric polynomials, J. London Math. Soc., (2) 53 (1996), 539-550.
  • Total positivity of the spline kernel and its applications, In: Total Positivity and its Applications (M. Gasca and C. Miccheli, Eds.), pp. 3-34, Kluwer, Dordrecht, 1996.
  • On a quadrature formula of Micchelli and Rivlin, J. Comp. Appl. Math. 70(1996), 349-356.
  • Gaussian quadrature formulae for Tchebycheff systems, East J. Approx. 3, 1(1997), 71-88.
  • On minimal cubature formulae for product weight functions, J. Comp. Appl. Math. 85 (1997), 113-121 (with G. Petrova).
  • Gaussian quadrature formula of Birkhoff's type, CALCOLO 34, 1-4 (1997), 41{50 (with Allal Guessab).
  • Remarks on the Jackson and Whitney constants, In: Recent Progress in Inequalities (G. Milovanović, Ed.), pp. 161-174, Kluwer Academic Publishers, Dordrecht, 1998.
  • Notes on miscellaneous approximation problems, In: Approximation Theory:In memory of A.K. Varma (Govil, Mohapatra, Nashed, Sharma, Szabados, Eds), pp. 97-113. Marcel Dekker, New York 1998.
  • Numerical integration over a disk. A new Gaussian quadrature formula, Numer. Math. 8, 1 (1998), 39-59 (with G. Petrova).
  • A note on the Hobby-Rice and Gauss-Krein theorems, East J. Approx. 4, 3(1998), 371-377.
  • On a formula of Obrechkoff, Annuaire Univ. Sofia, Fac. Math. Tome 89(1995), 19-21, Sofia, 1998.
  • Markov interlacing property for perfect splines, J. Approx. Theory 100, 2?(1999), 183-201.
  • Some examples of moment preserving approximation, in: Continued Fractions: From Analytic Number Theory to Constructive Approximation (B. Bernt and F. Gesztesy, Eds) Contemporary Mathematics, Volume 236, 1999, pp. 57-70 (with A. Sri Ranga).
  • Best one-sided L1-approximation by blending functions. In: Advances in Multivariate Approximation,; W. Haussmann, K. Jetter and M. Reimer (eds), Mathematical Research, Vol. 107, pp. 85-106, WILEY-VCH, Berlin, 1999 (with D,. Dryanov, W. Haussmann and G. Nikolov).
  • Moment preserving approximations, Mathematica Balkanica 13, 3-4 (1999), 385-398 (with Laura Gori).
  • An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös, J. d'Analyse Math. Vol. 78 (1999), 263-280 (with N. Naidenov).
  • Uniqueness of the Gaussian quadrature for a ball, J. Approx. Theory 104, 1 (2000), 21-44 (with G. Petrova).
  • Gaussian interval quadrature formula, Numer. Math., 87 (2001), 625-643 (with P. Petrov).
  • Gaussian extended cubature formulae for polyharmonic functions, Math. Comp. 70 (2001), 671-683 (with D. Dimitrov)
  • An extension of the Pizzetti formula for polyharmonic functions, Acta Math. Hungar. 91, 1-2 (2001), 99-113.
  • Bivariate polynomials of least deviation fromm zero, Canadian J. Math. 53, 3 (2001), 489-505 (with W. Haussmann and G. Nikolov).
  • Cubature formulae for polyharmonic functions, in: ISNM Vol. 137, Birkhäuser Verlag Basel/Switzerland, 2001, pp. 49-74.
  • Exact Makov-type inequalities for oscilating perfect splines, Constractive Approximation 18, 1(2002), 37-59 (with N. Naidenov).
  • On a Hermite interpolation by polynomials of two variables, SIAM J. Numer. Anal. 39, 5 (2002), 1780-1793 (with Yuan Xu).
  • Notes on miscellaneous problems, East J. Approx. 8, 1 (2002), 123-130.
  • Markov-type inequalities for polynomials and splines, in: Approximation Theory X: Abstract and Classical Analysis, Charles K. Chui, Larry L. Schumaker, and Joachim Stoeckler (eds.), pp. 31-90, Vanderbilt University Press, Nashville, TN, 2002.
  • Examples of Landau-Kolmogorov inequality in integral norms on a finite interval, J. Approx. Theory 117, 1 (2002), 55-73 (with N. Naidenov).
  • On polynomial interpolation of two variables, J. Approx. Theory 120(2003), 267-282 (with Yuan Xu).
  • Uniqueness of the Gaussian interval quadrature formula, Numer. Math. 95, 1 (2003), 53-62 (with P. Petrov).
  • Interpolation by bivariate polynomials based on Radon projections, Studia Mathematica 162, 2 (2004), 141-160 (with I. Georgieva).
  • Alternation property and Markov's inequality for Tchebycheff systems, East J. Approx. 10, 4 (2004), 481-503 (with N. Naidenov).
  • Majorization by polynomials on the plane, Indagationes Mathematicae, N. S., 15, 4 (2004), 469-483.
  • A quadrature formula of Gaussian type on the sphere, East J. Approx. 11, 2 (2005), 119-130 (with V. Gushev).
  • Gaussian interval quadrature formulae for Tchebycheff systems, SIAM J. Numer. Analysis 43, 2 (2005), 787-795 (with Petar Petrov).
  • Reconstruction of a polynomial from its Radon projections, SIAM J. Math. Analysis 37, 1 (2005), 238-250 (with Yuan Xu).
  • Quadrature formulae of non-standard type, Rendiconti di Matematica, Serie VII, Volume 25, Roma (2005), 195-221.
  • Optimal quadrature formulae, Uspehi Mat. Nauk 60, 6(2005), 33-52; English transl.: Russian Math. Surveys 60, 6(2005), 1035-1055.
  • Majorization of polynomials on the plane. II, East J. Approx. 12, 2(2006), 180-202 (with Nikola Naidenov).
  • Interpolation and integration based on averaged values, in: Approximation and Probability, Banach Center Publications, Volume 72, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2006, 25-47.