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:

  1. On the Error Formula for Ideal Interpolation [PDF]
  2. On the Limits Of Lagrange Projectors [PDF]

 

 

 

2007

 

  1. [PDF (07,1)] Bivariate Ideal Projectors and their Perturbations, Advances in Computational Mathematics
  2. [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
  3. [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 naďve 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.

 

 

2005

  1.  [PDF (1)] (with Skrzypek, Les\l aw), Uniqueness of minimal projections onto two-dimensional subspaces. Studia Math. 168 (2005), no. 3, 273--284.
  2.  [PDF (2)] Case study in bivariate Hermite interpolation. J. Approx. Theory 136 (2005), no. 2, 140--150.
  3.  [PDF (3)] Ideal projections onto planes. Approximation theory XI: Gatlinburg 2004, 395--404, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2005

 

2004

  1.  [PDF (1)] On Hermite interpolation in $R\sb d$. Electron. Trans. Numer. Anal. 18 (2004), 65—72.
  2.  [PDF (2)]Polynomial interpolation in $R\sb 3$. Comput. Math. Appl. 48 (2004), no. 9, 1299--1304.
  3.  [? PDF (3)] Interpolation by matrix-generated polynomials. Advances in constructive approximation: Vanderbilt 2003, 477--493, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2004.

 

2003

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

 

2002

  1.  [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.
  2.  [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.
  3.  [(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.

 

2001

  1.  [(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.
  2.  [PDF (2)] Obstacles to bounded recovery. Abstr. Appl. Anal. 6 (2001), no. 7, 381--400.
  3.  [PDF (3)] On the divergence of polynomial interpolation in the complex plane. Constr. Approx. 17 (2001), no. 3, 455--463.
  4.  [PDF (4)] (with Ivanov, Ivan V.), Linear discrete operators on the disk algebra. Proc. Amer. Math. Soc. 129 (2001), no. 7, 1987—1993
  5.  [PDF (5)] (with Chalmers, B. L.) A two-dimensional Hahn-Banach theorem. Proc. Amer. Math. Soc. 129 (2001), no. 3, 719—724

 

2000

  1.  [PDF (1)] On the density principle for rational functions. Numer. Algorithms 25 (2000), no. 1-4, 341—346.
  2.  [(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.
  3.  [PDF (3)] (with Chalmers, B. L.), Some estimates of action constants and related parameters. Comput. Math. Appl. 40 (2000), no. 1, 71--79.
  4.  [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.

 

1998

  1.  [(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. 
  2.  [(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.
  3.  [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.
  4.  [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
  5.  [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.
  6.   [(6)](with Chalmers, B.) Actions that characterize $l\sp {(n)}\sb \infty$. Linear Algebra Appl. 270 (1998), 155--169.

 

1997

  1.  [(1)](with Clark, W. E.) On the domination number of certain analogues of Kneser graphs. Congr. Numer. 126 (1997), 175--181.
  2.  [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.
  3.  [PS (3)] (with Clark, W. Edwin), Domination numbers of $q$-analogues of Kneser graphs. Bull. Inst. Combin. Appl. 19 (1997), 83--92.
  4.  [PDF (4)] (with Clark, W. Edwin), Covering by complements of subspaces. II. Proc. Amer. Math. Soc. 125 (1997), no. 1, 251--254.

 

1996

  1.  [PDF (1)] Another note on polynomial vs. rational approximation. J. Approx. Theory 85 (1996), no. 3, 343—347.
  2.  [PDF (2)] (with Chalmers, B. L.) Extension constants of unconditional two-dimensional operators. Linear Algebra Appl. 240 (1996), 173--182.

 

1995

  1.  [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.
  2.  [PS (2)] (with Clark, W. Edwin), Covering by complements of subspaces. Linear and Multilinear Algebra 40 (1995), no. 1, 1--13.
  3.  [(3)](with Clark, W. Edwin), On the domination matrices of the ${\scr C}$-analogues of Kneser graphs. Congr. Numer. 107 (1995), 193—197.
  4.  [PDF (4)](with Levin, Eli), Two problems on interpolation. Constr. Approx. 11 (1995), no. 4, 513--515.
  5.  [PDF (5)] Interpolation of individual functions. Concrete analysis. Comput. Math. Appl. 30 (1995), no. 3-6, 191--196.
  6.  [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.
  7.  [(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.

 

1994

  1.  [(1)] (with Chalmers, B. L.) The action constants. Approximation, probability, and related fields (Santa Barbara, CA, 1993), 161--166, Plenum, New York, 1994.
  2.  [(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.

 

1993

  1.  [(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.
  2.  [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.

 

1992

  1.  [(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.
  2.  [PDF (2)] Some Simple Open Problems on Interpolation of Individual Functions, Constructive Theory of Functions, Varna (1992), 259—268.
  3.  [(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.
  4.  [(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.
  5.  [PDF (5)] Discrete approximating operators on function algebras. Constr. Approx. 8 (1992), no. 3, 371--377.
  6.  [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.

 

1991

  1.  [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
  2.  [(2)] On polynomial "interpolation" in $L\sb 1$. J. Approx. Theory 66 (1991), no. 1, 24--28.
  3.  [(3)] (with Dyn, N.; Lubinsky, D. S.) On density of generalized polynomials. Canad. Math. Bull. 34 (1991), no. 2, 202--207.
  4.  [(4)] (with Pan, K. C.), On minimal interpolating projections and trace duality. J. Approx. Theory 65 (1991), no. 2, 216--230.

 

1990

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

 

1989

  1.  [PDF (1)] On rational bases. Approximation theory VI, Vol. II (College Station, TX, 1989), 589--592, Academic Press, Boston, MA, 1989.
  2.  [(2)] (with Gierz, Gerhard), On duality in rational approximation. Rocky Mountain J. Math. 19 (1989), no. 1, 137--143.

 

1988

  1.  [PDF (1)] On the norms of interpolating operators. Israel J. Math. 64 (1988), no. 1, 39--48.
  2.   [(2)] (with Gierz, Gerhard) On spaces with large Chebyshev subspaces. J. Approx. Theory 54 (1988), no. 2, 155--161.

 

1987

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

 

1986

  1.  [PDF (1)] (with Gierz, Gerhard) A duality principle for rational approximation. Pacific J. Math. 125 (1986), no. 1, 79--92.
  2.  [(2)] (with Newman, Donald J.), On isomorphisms with a prescribed range. J. Math. Anal. Appl. 117 (1986), no. 2, 299--302.
  3.  [(3)] On some problems of M. Z. Nashed on outer inverses. Linear Algebra Appl. 76 (1986), 149--152.
  4.  [PDF (4)] (with Gierz, Gerhard), On approximation by rationals from a hyperplane. Proc. Amer. Math. Soc. 96 (1986), no. 3, 452--454.

 

1985

  1.  [(1)] On projections in $L\sb 1$ and $L\sb \infty$. Constr. Approx. 1 (1985), no. 4, 297--303.
  2.  [PDF (2)] On the norms of some projections. Banach spaces (Columbia, Mo., 1984), 177--185, Lecture Notes in Math., 1166, Springer, Berlin, 1985.
  3.  [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.
  4.  [(4)] (with Newman, D. J.), A Losynski-Kharshiladze theorem for Müntz polynomials. Acta Math. Hungar. 45 (1985), no. 3-4, 301--303.

 

1984

  1.  [(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.

 

1983

  1.  [(1)] Some clas