Format:
Online-Ressource (XXIII, 564 p. 1 illus, online resource)
ISBN:
9780817680855
Series Statement:
Contemporary Mathematicians
Content:
Part 1. Publications of M. M. Schiffer -- Doctoral Students of M. M. Schiffer -- Chronology of M. M. Schiffer -- Part 2. Personal Reminiscences -- Paul R. Garabedian, “Recollections of Menahem Max Schiffer” -- Robert Finn, “Memories of Menahem Schiffer” -- Peter Duren, “Working with Max Schiffer” -- Lawrence Zalcman, “Memories of Max Schiffer” -- Dennis Hejhal, “Some Reminiscences of My Thesis Advisor, Max Schiffer” -- Dov Aharonov, “Max Schiffer at the Technion” -- Steven R. Bell, “M. M. Schiffer, Explorer” -- Part 3. Selected Papers -- Ein neuer Beweis des Endlichkeitssatzes f¨ur Orthogonalinvarianten -- Commentary by Lawrence Zalcman -- Sur un principe nouveau pour l’´evaluation des fonctions holomorphes -- Commentary by Peter Duren -- Sur un probl`eme d’extr´emum de la repr´esentation conforme -- A method of variation within the family of simple functions -- On the coefficients of simple functions -- Sur un th´eor`eme de la repr´esentation conforme -- Commentary by Peter Duren -- Sur la variation de la fonction de Green de domaines plans quelconques -- Sur la variation du diam`etre transfini -- Variation of the Green function and theory of the p-valued functions -- Commentary by Peter Duren -- The span of multiply connected domains -- Commentary by Brad Osgood -- Sur l’´equation diff´erentielle de M. L¨owner -- Commentary by Peter Duren -- Hadamard’s formula and variation of domain-functions -- Commentary by Peter Duren -- The kernel function of an orthonormal system -- Commentary by Dmitry Khavinson -- (with S. Bergman) A representation of Green’s and Neumann’s functions in the theory of partial differential equations of second order -- Commentary by Dmitry Khavinson -- (with S. Bergman) Kernel functions in the theory of partial differential equations of elliptic type -- Commentary by Dmitry Khavinson -- Faber polynomials in the theory of univalent functions -- Commentary by Peter Duren -- (with P. R. Garabedian) Identities in the theory of conformal mapping -- Commentary by Brad Osgood -- (with A. C. Schaeffer and D. C. Spencer) The coefficient regions of schlicht functions -- Commentary by Peter Duren -- (with P. R. Garabedian) On existence theorems of potential theory and conformal mapping -- Commentary by Brad Osgood -- (with S. Bergman) Kernel functions and conformal mapping -- Commentary by Dmitry Khavinson -- Variational methods in the theory of conformal mapping -- Commentary by Peter Duren -- [44] (with P. R. Garabedian and H. Lewy) Axially symmetric cavitational flow -- Commentary by Louis Nirenberg -- Variation of domain functional -- Commentary by Peter Duren -- (with P. R. Garabedian) A coefficient inequality for schlicht functions -- Commentary by Peter Duren.
Content:
M. M. Schiffer, the dominant figure in geometric function theory in the second half of the twentieth century, was a mathematician of exceptional breadth, whose work ranged over such areas as univalent functions, conformal mapping, Riemann surfaces, partial differential equations, potential theory, fluid dynamics, and the theory of relativity. He is best remembered for the powerful variational methods he developed and applied to extremal problems in a wide variety of scientific fields Spanning seven decades, the papers collected in these two volumes represent some of Schiffer's most enduring innovations. Expert commentaries provide valuable background and survey subsequent developments. Also included are a complete bibliography and several appreciations of Schiffer's influence by collaborators and other admirers.
Note:
Description based upon print version of record
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Preface; Contents; Publications of M. M. Schiffer; Doctoral Students of M. M. Schiffer; Chronology of Menahem Max Schiffer; Personal Reminiscences:; Recollections of Menahem Max Schiffer; Memories of Menahem Schiffer; Working with Max Schiffer; Memories of Max Schiffer; Some Reminiscences of My Thesis Advisor, Max Schiffer; Max Schiffer and the Technion; M. M. Schiffer, Explorer; Selected Papers:; Ein neuer Beweis des Endlichkeitssatzes für Orthogonalinvarianten; Commentary on; References; SUR UN PRINCIPE NOUVEAU POUR L'EVALUATION DES FONCTIONS BOLOMORPHES; Commentary on; References
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SUR UN PROBEME D'EXTREMUM DE LA REPRESENTATION CONFORMEA METHOD OF VARIATION WITHIN THE FAMILY OF SIMPLE FUNCTIONS; ON THE COEFFICIENTS OF SIMPLE FUNCTIONS; Sur un théorème de la représentation conforme; Commentary on; References; Sur la variation de la fonction de Green de domaines plans quelconques; SUR LA VARIATION DU DIAMETRE TRANSFINI; VARIATION OF THE GREEN FUNCTION AND THEORYOF THE p-VALUED FUNCTIONS; Commentary on; References; THE SPAN OF MULTIPLY CONNECTED DOMAINS; BIBLIOGRAPHY; Commentary on; References; Sur l'équation différentielle de M. Löwner; Commentary on; References
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HADAMARD'S FORMULA AND VARIATION OF DOMAIN-FUNCTIONS1. Hadamard's differential equation for Green's function.; 2. Further solutions of the variational equation (11).; 3. Applications of the variation formula to Green's function.; 4. The conformal radii dm (y).; 5. The construction of Ym(x; y) by means of Green's function.; 6. The functionals of a Riemann surface and their variation.; BIBLIOGRAPHY.; Commentary on; References; THE KERNEL FUNCTION OF AN ORTHONORMAL SYSTEM; BIBLIOGRAPHY; Commentary on; References
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A REPRESENTATION OF GREEN'S AND NEUMANN'S FUNCTIONS IN THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS OF SECOND ORDERBIBLIOGHAPHY; Commentary on; References; KERNEL FUNCTIONS IN THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS OF ELLIPTIC TYPE; BIBLIOGRAPHY; Commentary on; References; FABER POLYNOMIALS IN THE THEORY OF UNIVALENT FUNCTIONS; BIBLIOGRAPHY; Commentary on; References; IDENTITIES IN THE THEORY OF CONFORMAL MAPPING; BIBLIOGRAPHY; Commentary on; References; THE COEFFICIENT REGIONS OF SCHLICHT FUNCTIONS; REFERENCES; Commentary on; References
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ON EXISTENCE THEOREMS OF POTENTIAL THEORY AND CONFORMAL MAPPING1. Introduction; 2. Proof by orthogonalization over the domain; 3. Proof using the Dirichlet integral; 4. Proof by use of the boundary norm; 5. Method of minimum length; BIBLIOGRAPHY; Commentary on; References; Kernel functions and conformal mapping; Introduction.; 1. Generalities and notations.; 2. Green's function.; 3. The kernel functions.; 4. Identities and inequalities for the kernel functions.; 5. The l-transforms; 6. The eigen functions of the l-kernel; 7. Discussion of the eigen functions
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8. The space Λs. and its kernel functions.
Additional Edition:
ISBN 9780817636524
Additional Edition:
Druckausg. ISBN 978-081-763-652-4
Language:
English
DOI:
10.1007/978-0-8176-8085-5
URL:
Volltext
(lizenzpflichtig)
Author information:
Duren, Peter L. 1935-2020
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