In memoriam: Herbert Stahl August 3, 1942-April 22, 2013

After a prolonged and arduous fight with cancer, our beloved Herbert Robert Stahl1 died in his 71st year on April 22, 2013, in Berlin. Herbert was born on August 3, 1942, in Fehl-Ritzhausen, in the German state of RheinlandPfalz. At the age of 16, he started to work as an electrician for Allgemeine ElektricitätsGesellschaft (AEG, General Electricity Company), and by the time of his retirement in 2008 he established himself as one of the most prominent, respected, and honored mathematicians in approximation theory, orthogonal polynomials, and related fields. Before his university education, after working at AEG in 1958–1964, he became a sailor for a short time. His undergraduate, graduate, and postgraduate studies were all done at the Technische Universität Berlin (TUB) in the period 1965–1974. His Ph.D. (Dr. rer. nat.) dissertation in 1974, written under the supervision of Christian Pommerenke, was titled “Contributions to the convergence problem of Padé approximants”. Eventually he became an expert on Padé approximation, but his interest was wider, it included function theory, complex approximation, rational approximation, approximation with varying weights, and orthogonal polynomials. He obtained

[1]  Herbert Stahl,et al.  Quadratic Hermite-Padé polynomials associated with the exponential function , 2003, J. Approx. Theory.

[2]  E. Saff,et al.  Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1] , 1995 .

[3]  H. Stahl.  Asymptotic Distributions of Zeros of Quadratic Hermite–Pade Polynomials Associated with the Exponential Function , 2006 .

[4]  Herbert Stahl,et al.  The structure of extremal domains associated with an analytic function , 1985 .

[5]  Herbert Stahl,et al.  Diagonal Padé approximants to hyperelliptic functions , 1996 .

[6]  Herbert Stahl,et al.  On the convergence of generalized Padé approximants , 1989 .

[7]  J. Nuttall,et al.  THE CONVERGENCE OF PADÉ APPROXIMANTS TO FUNCTIONS WITH BRANCH POINTS , 1977 .

[8]  Herbert Stahl,et al.  Convergence of Rational Interpolants ∗ , 1996 .

[9]  D. Lubinsky,et al.  What distributions of points are possible for convergent sequences of interpolatory integration rules? , 1993 .

[10]  Andrei Aleksandrovich Gonchar (on his 80th birthday) , 2011 .

[11]  V. Totik,et al.  Nth Root Root Asymptotic Behavior of Orthonormal Polynomials , 1990 .

[12]  Box-Jenkins Analysis of Air Pollution Data , 1988 .

[13]  H. Stahl.  Asymptotics of Hermite-Padé Polynomials and Related Convergence Results — A Summary of Results , 1988 .

[14]  Laurent Baratchart,et al.  Asymptotic Error Estimates for L2 Best Rational Approximants to Markov Functions , 2001, J. Approx. Theory.

[15]  Herbert Stahl,et al.  Spurious poles in Pade´ approximation , 1998 .

[16]  D. Lubinsky,et al.  Some Explicit Biorthogonal Polynomials , 2005 .

[17]  Divergence of diagonal Padé approximants and the asymptotic behavior of orthogonal polynomials associated with nonpositive measures , 1985 .

[18]  Herbert Stahl.  The convergence of diagonal Padé approximants and the Padé conjecture , 1997 .

[19]  Herbert Stahl,et al.  Uniform rational approximation of |X| , 1993 .

[20]  Laurent Baratchart,et al.  WEIGHTED EXTREMAL DOMAINS AND BEST RATIONAL APPROXIMATION , 2011 .

[21]  Herbert Stahl,et al.  Orthogonal polynomials with complex-valued weight function, I , 1986 .

[22]  D. Lubinsky,et al.  Distribution of points for convergent interpolatory integration rules on (−∞, ∞) , 1993 .

[23]  Doron S. Lubinsky,et al.  Interpolatory integration rules and orthogonal polynomials with varying weights , 1992, Numerical Algorithms.

[24]  H. Stahl.  Poles and zeros of best rational approximants of |x| , 1994 .

[25]  Laurent Baratchart,et al.  Non-uniqueness of rational best approximants , 1999 .

[26]  A. Aptekarev,et al.  Asymptotics of Hermite-Padé Polynomials , 1992 .

[27]  Herbert Stahl,et al.  Best uniform rational approximation ofxα on [0, 1] , 2003 .

[28]  K. Driver,et al.  Simultaneous Rational Approximants to Nikishin Systems of Two Functions , 1995 .

[29]  Bernstein type inequalities for derivatives of rational functions in $ L_p$ spaces for $ p<1$ , 1995 .

[30]  Doron S. Lubinsky,et al.  Asymptotic zero distribution of biorthogonal polynomials , 2015, J. Approx. Theory.

[31]  Herbert Stahl.  Best uniform rational approximation of $x^\alpha$ on $[0,1]$ , 1993 .

[32]  L. J. Heider.  A NOTE ON A THEOREM OF , 1957 .

[33]  Herbert Stahl,et al.  Orthogonal polynomials with complex-valued weight function, II , 1986 .

[34]  K. Driver,et al.  Normality and Error Formulae for Simultaneous Rational Approximants to Nikishin Systems , 1994 .

[35]  H. Stahl,et al.  Proof of the BMV conjecture , 2011, 1107.4875.

[36]  Vilmos Totik,et al.  General Orthogonal Polynomials , 1992 .

[37]  H. Stahl.  Existence and uniqueness of rational interpolants with free and prescribed poles , 1987 .

[38]  D. Lubinsky,et al.  Distribution of Points in Convergent Sequences of Interpolatory Integration Rules: The Rates , 1993 .

[39]  Walter Van Assche,et al.  Type II HermitePad approximation to the exponential function , 2005 .

[40]  Herbert Stahl,et al.  Three different approaches to a proof of convergence for Padé approximants , 1987 .

[41]  H. Stahl,et al.  Sets of Minimal Capacity and Extremal Domains , 2012, 1205.3811.

[42]  H. Stahl.  Simultaneous Rational Approximants , 1995 .

[43]  Herbert Stahl,et al.  From Taylor to quadratic Hermite-Padé polynomials. , 2006 .

[44]  D. Bessis,et al.  Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics , 1975 .

[45]  K. Driver,et al.  Normality in Nikishin systems , 1994 .

[46]  Herbert Stahl,et al.  Extremal domains associated with an analytic function I , 1985 .

[47]  Laurent Baratchart,et al.  Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in L 2 of the Circle , 1998 .

[48]  Herbert Stahl,et al.  An extension of the ' 1/9 '-problem , 2009, J. Comput. Appl. Math..

[49]  Herbert Stahl.  Conjectures around the baker-gammel-wills conjecture , 1997 .

[50]  D. Newman.  Rational approximation to | x , 1964 .

[51]  Edward B. Saff,et al.  Support of the logarithmic equilibrium measure on sets of revolution in R3 , 2007 .