Selected Papers (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
682
Utgivningsdatum
2013-01-31
Upplaga
Reprint 2013 of the 2000 edition
Förlag
Springer-Verlag New York Inc.
Medarbetare
Rivlin, Theodore J. (red.)/Saff, Edward B. (red.)
Illustrationer
2 black & white illustrations, biography
Dimensioner
234 x 156 x 37 mm
Vikt
1003 g
Antal komponenter
1
Komponenter
Paperback
ISBN
9781461461326
Selected Papers (häftad)

Selected Papers

Häftad Engelska, 2013-01-31
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This volume is a selection from the 281 published papers of Joseph Leonard Walsh, former US Naval Officer and professor at University of Maryland and Harvard University. The nine broad sections are ordered following the evolution of his work. Commentaries and discussions of subsequent development are appended to most of the sections. Also included is one of Walsh's most influential works, "A closed set of normal orthogonal function," which introduced what is now known as "Walsh Functions".
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From the reviews: MATHEMATICAL REVIEWS "Because of Walsh's chairmanship of the Mathematics Department at Harvard and of the American Mathematical Society, and the very substantial impact of his doctoral students, this material will be a valuable resource for those interested in the development of American mathematics...an essential reference. No doubt all those interested in constructive or geometric function theory, complex approximation,...will also find a place for it on their shelves."

Övrig information

Joseph Leonard Walsh (1895-1973) was an American mathematician. For most of his professional career he studied and worked at Harvard University. He received a B.S. in 1916 and a PhD in 1920. The Advisor of his PhD was Maxime Bocher. He started to work as lecturer in Harvard afterwards and became a full professor in 1935. With two different scholarships he was able to study in Paris under Paul Montel (1920-21) and in Munich under Constantin Caratheodory (1925-26). From 1937 to 1942 he served as chairman of his department at Harvard. During World War II he served as an officer in the US navy and was promoted to captain right after end of the war. After his retirement from Harvard in 1966 he accepted a position at the University of Maryland where he continued to work up to a few months before his death. Joseph L. Walsh became a member of the National Academy of Sciences in 1936 and served 1949-51 as president of the American Mathematical Society. Altogether he published 279 articles (research and others), seven books and advised 31 PhD students. The Walsh function and the Walsh-Hadamard code are named after him. The Grace-Walsh-Szego Coincidence Theorem is important in the study of the location of the zeros of multivariate polynomials.

Innehållsförteckning

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*] Uber die Entwicklung einer analytischen Funktion nach Polynomen.- [26-c*] Uber die Entwicklung einer Funktion einer komiexen Veranderlichen 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*] Uber 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. Holder 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'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