University of South Florida

Shekhtman, Boris.

PUBLICATIONS by year

Submitted:

a) On a Variation of one Example of A. Iarrobino [PDF (E4)]

b) (with Skrzypek Les\low), On Non-uniqueness of Minimal Projections in L_p spaces. [PDF (E5)]

c) (with Carl de Boor), On the pointwise limits of bivariate Lagrange projectors. [PDF (E6)]

d) (with Tom McKinley), On Simultaneous Block-Diagonalization of Cyclic Commuting Matrices. [PDF (E7)]

e) On Real Solutions for System of Polynomial Equations. [PDF]

f) (with Tom McKinley), What do the Real Ideal Projectors Interpolate. [PDF]

g) On a Conjecture of Tomas Sauer Regarding Nested Ideal Interpolation. [PDF]

To appear:

On the Error Formula for Ideal Interpolation [PDF]

On the Limits Of Lagrange Projectors [PDF]

2007

[PDF (07,1)] Bivariate Ideal Projectors and their Perturbations, Advances in Computational Mathematics

[PDF (07,2)](with Ma W-X), A Linear System Arising from a Polynomial Problem, Chin. Ann. Math, Volume 28B, number 3, (2007), 283—292

[PDF (E1)] On Perturbation of Ideal Complements, In Banach Spaces and their Applications in Analysis, B. Randrianantonina and N. Randrianantonina eds. De Gruyter, Berlin-New York (2007), 413--422

2006

1 [PDF (1)]On a Conjecturs of Carl de Boor Regarding the Limits of Lagrange Interpolants, Constructive Approximation, Volume 24, Number 3, (2006), 365—370

2 [PDF (2)]On the naïve error formula for bivariate linear interpolation. Wavelets and splines: Athens 2005, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2006, 416—427

3 [PDF (3)] (with Rakhmanov, Evguenii) On discrete norms of polynomials. J. Approx. Theory 139 (2006), no. 1-2, 2—7

4 [PDF (4)]Uniqueness of Tchebysheff Spaces and their Ideal Relatives, Frontiers in Interpolation and Approximation, Pure and Applied Mathematics, Chapman&Hall, (2006), 407—425.

5 [PDF, (5)]On one Question of Ed Saff, Elec. Trans. Numer. Anal., Vol 25, (2006), 439—445.

6 [PDF (6)] (with Skrzypek, Les\l aw), Norming points and unique minimality of orthogonal projections. Abstr. Appl. Anal. 2006, 1—17.

7 [PDF (7)] (with Skrzypek, Les\l aw), Geometric Aspects of minimal Projections onto Plains, Constructive Theory of Functions, Varna 2005 (B.D. Bojanov ed.), Martin Drinov Academic Publishing House, (2006), 267—277.

10 2005

11 [PDF (1)] (with Skrzypek, Les\l aw), Uniqueness of minimal projections onto two-dimensional subspaces. Studia Math. 168 (2005), no. 3, 273--284.

12 [PDF (2)] Case study in bivariate Hermite interpolation. J. Approx. Theory 136 (2005), no. 2, 140--150.

13 [PDF (3)] Ideal projections onto planes. Approximation theory XI: Gatlinburg 2004, 395--404, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2005

15 2004

16 [PDF (1)] On Hermite interpolation in $R\sb d$. Electron. Trans. Numer. Anal. 18 (2004), 65—72.

17 [PDF (2)]Polynomial interpolation in $R\sb 3$. Comput. Math. Appl. 48 (2004), no. 9, 1299--1304.

18 [? PDF (3)] Interpolation by matrix-generated polynomials. Advances in constructive approximation: Vanderbilt 2003, 477--493, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2004.

20 2003

21 [PDF (1)] (with Chalmers, B. L.; Ostrovskii, M. I.), Hahn-Banach operators: a review. J. Comput. Anal. Appl. 5 (2003), no. 1, 11—24.

23 2002

24 [PDF (1)]On interpolation by and Banach spaces of polynomials. Paul Erdös and his mathematics, I (Budapest, 1999, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, 2002, ), 637—652.

25 [PDF(2)]Interpolation by polynomials in several variables. Approximation theory, X (St. Louis, MO, 2001), 367--372, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 2002.

26 [(3)] (with Chalmers, Bruce L.), On spaces admitting minimal projections which are orthogonal. Approximation theory, X (St. Louis, MO, 2001), 113--116, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 2002.

28 2001

29 [(1)] (with Chalmers, B. L.), On minimal, almost locally minimal, and orthogonal minimal projections. Trends in approximation theory (Nashville, TN, 2000), 49--52, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 2001.

30 [PDF (2)] Obstacles to bounded recovery. Abstr. Appl. Anal. 6 (2001), no. 7, 381--400.

31 [PDF (3)] On the divergence of polynomial interpolation in the complex plane. Constr. Approx. 17 (2001), no. 3, 455--463.

32 [PDF (4)] (with Ivanov, Ivan V.), Linear discrete operators on the disk algebra. Proc. Amer. Math. Soc. 129 (2001), no. 7, 1987—1993

33 [PDF (5)] (with Chalmers, B. L.) A two-dimensional Hahn-Banach theorem. Proc. Amer. Math. Soc. 129 (2001), no. 3, 719—724

35 2000

36 [PDF (1)] On the density principle for rational functions. Numer. Algorithms 25 (2000), no. 1-4, 341—346.

37 [(2)](with Chalmers, B. L.; Metcalf, F. T.), On the computation of minimal projections: millennium report. Applied mathematics reviews, Vol. 1, 119--156, World Sci. Publ., River Edge, NJ, 2000.

38 [PDF (3)] (with Chalmers, B. L.), Some estimates of action constants and related parameters. Comput. Math. Appl. 40 (2000), no. 1, 71--79.

39 [PDF (4)] (with Chalmers, B.; Cottin, C.), Minimal Boolean sum and blending-type projections and extensions. Comput. Math. Appl. 40 (2000), no. 1, 63--70.

41 1998

42 [(1)]On the discrete norms of polynomials. Approximation theory IX, Vol. I. (Nashville, TN, 1998), 303--307, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 1998.

43 [(2)](with Ivanov, Ivan), Linear discrete operators and recovery of functions. Approximation theory IX, Vol. I. (Nashville, TN, 1998), 157--164, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 1998.

44 [PDF (3)] (with Chalmers, B. L.), Spectral properties of operators that characterize $l\sp {(n)}\sb \infty$. Abstr. Appl. Anal. 3 (1998), no. 3-4, 237—246.

45 [PS (4)] (with Clark, W. Edwin; Suen, Stephen; Fisher, David C.) Upper bounds for the domination number of a graph. Congr. Numer. 132 (1998), 99—123

46 [PDF (5)] (with Clark, W. Edwin; McColm, Gregory L.) An application of spanning trees to $k$-point separating families of functions. J. London Math. Soc. (2) 58 (1998), no. 2, 297--310.

47 [(6)](with Chalmers, B.) Actions that characterize $l\sp {(n)}\sb \infty$. Linear Algebra Appl. 270 (1998), 155--169.

49 1997

50 [(1)](with Clark, W. E.) On the domination number of certain analogues of Kneser graphs. Congr. Numer. 126 (1997), 175--181.

51 [PDF (2)]On the strong form of the Faber theorem. Stochastic processes and functional analysis (Riverside, CA, 1994), 215--218, Lecture Notes in Pure and Appl. Math., 186, Dekker, New York, 1997.

52 [PS (3)] (with Clark, W. Edwin), Domination numbers of $q$-analogues of Kneser graphs. Bull. Inst. Combin. Appl. 19 (1997), 83--92.

53 [PDF (4)] (with Clark, W. Edwin), Covering by complements of subspaces. II. Proc. Amer. Math. Soc. 125 (1997), no. 1, 251--254.

55 1996

56 [PDF (1)] Another note on polynomial vs. rational approximation. J. Approx. Theory 85 (1996), no. 3, 343—347.

57 [PDF (2)] (with Chalmers, B. L.) Extension constants of unconditional two-dimensional operators. Linear Algebra Appl. 240 (1996), 173--182.

59 1995

60 [PDF(1)]On simultaneous interpolation of two functions. Approximation theory VIII, Vol. 1 (College Station, TX, 1995), 515--518, Ser. Approx. Decompos., 6, World Sci. Publ., River Edge, NJ, 1995.

61 [PS (2)] (with Clark, W. Edwin), Covering by complements of subspaces. Linear and Multilinear Algebra 40 (1995), no. 1, 1--13.

62 [(3)](with Clark, W. Edwin), On the domination matrices of the ${\scr C}$-analogues of Kneser graphs. Congr. Numer. 107 (1995), 193—197.

63 [PDF (4)](with Levin, Eli), Two problems on interpolation. Constr. Approx. 11 (1995), no. 4, 513--515.

64 [PDF (5)] Interpolation of individual functions. Concrete analysis. Comput. Math. Appl. 30 (1995), no. 3-6, 191--196.

65 [PDF (6)] Interpolating subspaces in $\bold R\sb n$. Interpolating at two and three points. Approximation theory, wavelets and applications (Maratea, 1994), 465--471, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995.

66 [(7)](with Borwein, P. B.) Corrigendum: "The density of rational functions in Markov systems: a counterexample to a conjecture of D. J. Newman" [Constr. Approx. 9 (1993), no. 1, 105--110;]. Constr. Approx. 11 (1995), no. 1, 139.

68 1994

69 [(1)] (with Chalmers, B. L.) The action constants. Approximation, probability, and related fields (Santa Barbara, CA, 1993), 161--166, Plenum, New York, 1994.

[(2)] (with Chalmers, B. L.) On the role of $l\sb \infty$ in approximation theory. Approximation, probability, and related fields (Santa Barbara, CA, 1993), 151--160, Plenum, New York, 1994.

1 1993

[(1)]Duality principle in linearized rational approximation. Methods of approximation theory in complex analysis and mathematical physics (Leningrad, 1991), 173--177, Lecture Notes in Math., 1550, Springer, Berlin, 1993.

1 [PDF (2)] (with Borwein, Peter B.), The density of rational functions in Markov systems: a counterexample to a conjecture of D. J. Newman. Constr. Approx. 9 (1993), no. 1, 105--110.

3 1992

[(1)] (with Chalmers, B. L.; Pan, K. C.), When is the adjoint of a minimal projection also minimal. Approximation theory (Memphis, TN, 1991), 217--226, Lecture Notes in Pure and Appl. Math., 138, Dekker, New York, 1992.

1 [PDF (2)] Some Simple Open Problems on Interpolation of Individual Functions, Constructive Theory of Functions, Varna (1992), 259—268.

2 [(3)](with Chalmers, B. L.; Pan, K. C.) A strategy for proving extensions of the $4/3$ conjecture. Approximation theory (Memphis, TN, 1991), 207--215, Lecture Notes in Pure and Appl. Math., 138, Dekker, New York, 1992.

3 [(4)] Some examples concerning projection constants. Approximation theory, spline functions and applications (Maratea, 1991), 471--476, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 356, Kluwer Acad. Publ., Dordrecht, 1992.

[PDF (5)] Discrete approximating operators on function algebras. Constr. Approx. 8 (1992), no. 3, 371--377.

1 [PDF (6)] (with Gierz, Gerhard),On Archimedean ordered vector spaces and a characterization of simplices. Proc. Amer. Math. Soc. 116 (1992), no. 2, 369--375.

3 1991

4 [PDF (1)] Some idempotent matrices of large rank. Approximation interpolation and summability (Ramat Aviv, 1990/Ramat Gan, 1990), 261--266, Israel Math. Conf. Proc., 4, Bar-Ilan Univ., Ramat Gan, 1991

5 [(2)] On polynomial "interpolation" in $L\sb 1$. J. Approx. Theory 66 (1991), no. 1, 24--28.

6 [(3)] (with Dyn, N.; Lubinsky, D. S.) On density of generalized polynomials. Canad. Math. Bull. 34 (1991), no. 2, 202--207.

7 [(4)] (with Pan, K. C.), On minimal interpolating projections and trace duality. J. Approx. Theory 65 (1991), no. 2, 216--230.

9 1990

10 [(1)] (with Saff, E. B.), Interpolatory properties of best $L\sb 2$-approximants. Indag. Math. (N.S.) 1 (1990), no. 4, 489--498.

11 [PDF (2)] On a problem of G. G. Lorentz regarding the norms of Fourier projections. Proc. Amer. Math. Soc. 108 (1990), no. 1, 187--190.

13 1989

14 [PDF (1)] On rational bases. Approximation theory VI, Vol. II (College Station, TX, 1989), 589--592, Academic Press, Boston, MA, 1989.

[(2)] (with Gierz, Gerhard), On duality in rational approximation. Rocky Mountain J. Math. 19 (1989), no. 1, 137--143.

1 1988

2 [PDF (1)] On the norms of interpolating operators. Israel J. Math. 64 (1988), no. 1, 39--48.

3 [(2)] (with Gierz, Gerhard) On spaces with large Chebyshev subspaces. J. Approx. Theory 54 (1988), no. 2, 155--161.

5 1987

6 [(1)] On the geometry of real polynomials. Approximation theory, Tampa (Tampa, Fla., 1985--1986), 161--175, Lecture Notes in Math., 1287, Springer, Berlin, 1987.

8 1986

[PDF (1)] (with Gierz, Gerhard) A duality principle for rational approximation. Pacific J. Math. 125 (1986), no. 1, 79--92.

[(2)] (with Newman, Donald J.), On isomorphisms with a prescribed range. J. Math. Anal. Appl. 117 (1986), no. 2, 299--302.

1 [(3)] On some problems of M. Z. Nashed on outer inverses. Linear Algebra Appl. 76 (1986), 149--152.

2 [PDF (4)] (with Gierz, Gerhard), On approximation by rationals from a hyperplane. Proc. Amer. Math. Soc. 96 (1986), no. 3, 452--454.

4 1985

5 [(1)] On projections in $L\sb 1$ and $L\sb \infty$. Constr. Approx. 1 (1985), no. 4, 297--303.

6 [PDF (2)] On the norms of some projections. Banach spaces (Columbia, Mo., 1984), 177--185, Lecture Notes in Math., 1166, Springer, Berlin, 1985.

7 [PDF (3)] (with Chalmers, Bruce L.), Minimal projections and absolute projection constants for regular polyhedral spaces. Proc. Amer. Math. Soc. 95 (1985), no. 3, 449—452.

8 [(4)] (with Newman, D. J.), A Losynski-Kharshiladze theorem for Müntz polynomials. Acta Math. Hungar. 45 (1985), no. 3-4, 301--303.

10 1984

11 [(1)]On projections in approximation theory. Approximation theory and spline functions (St. John's, Nfld., 1983), 455--466, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 136, Reidel, Dordrecht, 1984.

13 1983

79. [(1)] Some classification schemes in approximation theory. Approximation theory, IV (College Station, Tex., 1983), 673--678, Academic Press, New York, 1983.

[(2)] Interpolation projections and Banach spaces. J. Approx. Theory 38 (1983), no. 4, 338--343.

1 1982

[(1)] Properties of spline projections. Multivariate approximation theory, II (Oberwolfach, 1982), 375--384, Internat. Ser. Numer. Math., 61, Birkhäuser, Basel, 1982.

1 [(2)] Why piecewise linear functions are dense in $C[0,\,1]$. J. Approx. Theory 36 (1982), no. 3, 265--267.

3 1980

[(1)] Unconditional convergence of abstract splines. J. Approx. Theory 30 (1980), no. 3, 237--246.

83. [(2)] Some remarks on approximation in $C(\Omega )$. Approximation theory, III (Proc. Conf., Univ. Texas, Austin, Tex., 1980), pp. 829--836, Academic Press, New York-London, 1980.

[(3)] The limits of abstract splines. Numer. Funct. Anal. Optim. 2 (1980), no. 5, 375--385.

1 1978

[(1)] (as\v Sehtman, B.) Abstract interpolation theory. (Russian) Tartu Riikl. Ül. Toimetised No. 448 (1978), 82--93.

1977

[(1)] (as \v Sehtman, B.), Abstract Interpolation Theory, (Russian) Proc. Of Student Conference of Baltic Republics, (1997), 78—79.

[(2)] (as\vSehtman,B.) Interpolation in Hilbert Spaces, (Russian) Pros. Of Petrapavlovsk Student Conference, (1977), 56—57.