Bernstein-Markov: a survey

We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.

[1]  E. Saff,et al.  Logarithmic Potentials with External Fields , 1997 .

[2]  L. Bos,et al.  On the Convergence of Optimal Measures , 2008 .

[3]  Jean-Paul Calvi,et al.  Uniform approximation by discrete least squares polynomials , 2008, J. Approx. Theory.

[4]  Thomas Bloom,et al.  Random polynomials and (pluri)potential theory , 2007 .

[5]  Rene F. Swarttouw,et al.  Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.

[6]  T. Bloom,et al.  Transfinite diameter notions in ℂN and integrals of Vandermonde determinants , 2007, 0712.2844.

[7]  C. Brezinski.  General orthogonal polynomials , 1980 .

[8]  Thomas Bloom,et al.  ZEROS OF RANDOM POLYNOMIALS ON C m , 2006 .

[9]  T. Bloom,et al.  Modified logarithmic potential theory and applications , 2015 .

[10]  Alvise Sommariva,et al.  Computing approximate Fekete points by QR factorizations of Vandermonde matrices , 2009, Comput. Math. Appl..

[11]  Turgay Bayraktar,et al.  Equidistribution of zeros of random holomorphic sections , 2013, 1312.0933.

[12]  Thomas Bloom,et al.  Random Polynomials and Pluripotential-Theoretic Extremal Functions , 2013, 1304.4529.

[13]  Robert Berman,et al.  Fekete points and convergence towards equilibrium measures on complex manifolds , 2009, 0907.2820.

[14]  Federico Piazzon,et al.  Some Results on the Rational Bernstein–Markov Property in the Complex Plane , 2015, 1502.03256.

[15]  Matt Davis,et al.  Transfinite Diameter , 2004 .

[16]  V P Zaharjuta,et al.  TRANSFINITE DIAMETER, ČEBYŠEV CONSTANTS, AND CAPACITY FOR COMPACTA IN , 1975 .

[17]  Tom Bloom,et al.  Pluripotential energy and large deviation , 2011, 1110.6593.

[18]  T. Bloom,et al.  Vector energy and large deviation , 2013 .

[19]  Thomas Bloom,et al.  ZEROS OF RANDOM POLYNOMIALS ON C , 2007 .

[20]  T. Bloom,et al.  Logarithmic Potential Theory and Large Deviation , 2014 .

[21]  Thomas Ransford,et al.  Potential Theory in the Complex Plane: Bibliography , 1995 .

[22]  A Sadullaev.  AN ESTIMATE FOR POLYNOMIALS ON ANALYTIC SETS , 1983 .

[23]  Robert Berman,et al.  Growth of balls of holomorphic sections and energy at equilibrium , 2008, 0803.1950.

[24]  Thomas Bloom,et al.  Asymptotics for Christoffel functions of planar measures , 2008 .

[25]  Thomas Bloom.  Random polynomials and Green functions , 2005 .

[26]  Thomas Bloom,et al.  Capacity convergence results and applications to a Berstein-Markov inequality , 1999 .

[27]  Thomas Bloom.  Orthogonal polynomials in C^n , 1997 .

[28]  J. L. Ullman,et al.  Weak limits of zeros of orthogonal polynomials , 1986 .