Walsh, Joseph L. 　著

内容

目次

1 Zeros and Critical Points of Polynomials and Rational Functions.- [18*] On the location of the roots of the Jacobian of two binary forms and of the derivative of a rational function.- [21-a*] On the location of the roots of the derivative of a polynomial.- [21-b*] On the location of the roots of the Jacobian of two binary forms and of the derivative of a rational function.- [20-c*] On the location of the roots of the derivative of a polynomial.- [33-1*] Note on the location of the roots of the derivative of a polynomial.- [22-g*] On the location of the roots of certain types of polynomials.- [64-e*] A Theorem of Grace on the zeros of polynomials, revisited.- [64-j*] The location of the zeros of the derivative of a rational function, revisited.- [24-h*] An inequality for the roots of an algebraic equation.- Commentary.- Comments on [18*], [21-a*], and [21-b*].- Comments on [20-c*] and [33-i*].- Comments on [22-g*].- Editors’ Note.- Comments on [64-e*], [64-j*].- Comments on [24-h*].- 2 Walsh Functions.- [23-b*] A closed set of normal orthogonal functions.- Commentary.- The Walsh System.- The Impact of Walsh Functions on Modern Mathematics.- Probability Theory.- Harmonic Analysis.- Functional Analysis.- Generalizations.- Technical Applications.- Commentary by T. J. Rivlin.- 3 Qualitative Approximation.- [26-b*] Über die Entwicklung einer analytischen Funktion nach Polynomen.- [26-c*] Über die Entwicklung einer Funktion einer komiexen Veränderlichen nach Polynomen.- [28-a*] On the expansion of analytic functions in series of polynomials and in series of polynomials and in series of other analytic functions.- [28-d*] Über die Entwicklung einer harmonischen Funktion nach harmonischen Polynomen.- [29-b*] The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions.- Commentary.- 4 Conformai Mapping.- [37-d*] On the shape of level curves of Green’s function.- [38-a*] Note on the curvature of orthogonal trajectories of level curves of Green’s functions.- [39-d*] On the circles of curvature of the images of circles under a conformal map.- [40-a*] Note on the curvature of the orthogonal trajectories of level curves of Green’s functions.- [70-a*] On the shape of the level loci of harmonic measure.- [55-a*] (With D. Gaier) Zur Methode der variablen Gebiete bei der Randverserrung.- [56-b*] (With L. Rosenfeld) On the boundary behavior of a conformal map.- [56-d*] On the conformal mapping of multiply connected regions.- Commentary Dieter Gaier.- Topic I: Geometry of level curves and related topics.- I.1. Domains convex in one direction.- I.2. Length and area problems.- I.3. On the geometry of lemniscates.- Topic II: Conformal mapping near the boundary.- II.1. Conformal mapping of strip domains.- II.2. Hölder continuity of the mapping function.- Topic III: Conformal mapping of multiply connected domains.- III. 1. Walsh’s new canonical map.- III. 2. New approaches to Walsh’s theorem.- III. 3. General canonical domains.- 5 Polynomial Approximation.- [32-c*] On polynomial interpolation to analytic functions with singularities.- [37-g*] (With W.E. Sewell) Note on the relation between continuity and degree of polynomial approximation in the complex domain.- [38-d*] (With W.E. Sewell) Note on degree of trigonometric and polynomial approximation to an analytic function.- [53-c*] (With T.S. Motzkin) On the derivative of a polynomial and Chebyshev approximation.- [73-a*] (With T.S. Motzkin) Equilibrium of inverse-distance forces in three-dimensions.- [34-c*] Note on the orthogonality of Tchebycheff polynomials on confocal ellipses.- [42-a*] Note on the coefficients of overconvergent power series.- [51-c*] Note on approximation by bounded analytic functions.- [68-e*] Approximation by bounded analytic functions: Uniform convergence as implied by mean convergence.- [73-c*] History of the Riemann mapping theorem.- Commentary.- Comments on [32-c*].- Comments on [37-g*] and [38-d*].- Comments on [53-c*] and [73-a*].- Comments on [34-c*].- Comments on [42-a*].- Comments on [51-c*].- Comments on [73-c*].- 6 Rational Approximation 465.- [31-c*] On the overconvergence of certain sequences of rational functions of best approximation.- [34-b*] On approximation to an analytic function by rational functions of best approximation.- [40-b*] On the degree of convergence of sequences of rational functions.- [46-c*] Overconvergence, degree of convergence, and zeros of sequences of analytic functions.- [64-a*] Padé approximants as limits of rational functions of best approximation.- [65-i*] The convergence of sequences of rational functions of best approximation with some free poles.- [67-c*] An extension of the generalized Bernstein lemma.- [68-a*] Degree of approximation by rational functions and polynomials.- [71-b*] (With Dov Aharonov) Some examples in degree of approximation by rational functions.- Commentary.- Comments on [31-c*].- Comments on [34-b*].- Comments on [40-b*].- Comments on [46-c*].- Comments on [64-a*].- Comments on [65-i*].- Comments on [67-c*].- Comments on [68-a*].- Comments on [71-b*].- 7 Spline Functions.- [65-b*] (With J.H. Ahlberg and E.N. Nilson) Fundamental properties of generalized splines.- [67-d*] (With J.H. Ahlberg and E.N. Nilson) Complex cubic splines.- [68-f*] (With J.H. Ahlberg and E.N. Nilson) Cubic splines on the real line.- Commentary by Walter Schempp.