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Menahem Max Schiffer Selected Papers, Volume 1

Peter Duren and Lawrence Zalcman, editors
Publication Date: 
Number of Pages: 
Contemporary Mathematicians
[Reviewed by
Charles Ashbacher
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One does not have to read very many of the papers in this collection to be extremely impressed by the mathematical and writing abilities of Menachem Schiffer. The combined thickness of these two volumes as well as the use of the word “selected” in the title strongly reinforces this impression.

Volume 1 opens with a list of the Schiffer publications, the doctoral students of Schiffer, a chronology of his life and a series of very brief testimonials to Schiffer. Given his impact on mathematics, it is surprising that only 10 pages are devoted to this topic.

The remainder is devoted to reprints of Schiffer’s papers, some of which appear in the original German and French although the majority are in English. Most are followed by a commentary that is in English and approximately one page in length.

Many books about people that had a significant impact on mathematics have a great deal of ink devoted to the person. That is not the case here. Reading these books will expose you to the mathematical output of Menachem Schiffer, but you will learn very little about his life. Given that he left Germany for Palestine in 1933 as a consequence of the rise of the Nazi Party in Germany, there are no doubt some very interesting stories that could be told. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

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 für Orthogonalinvarianten
    Commentary by Lawrence Zalcman
Sur un principe nouveau pour l’évaluation des fonctions holomorphes
    Commentary by Peter Duren
Sur un problème d’extrémum de la représentation conforme
A method of variation within the family of simple functions
On the coefficients of simple functions
Sur un théorème de la représentation conforme
    Commentary by Peter Duren
Sur la variation de la fonction de Green de domaines plans quelconques
Sur la variation du diamètre 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’équation différentielle de M. Löwner
    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.

Comments's picture

Readers who share the concerns expressed by the reviewer in his final paragraph will undoubtedly find the semi-autobiographical piece with which Volume 2 concludes of particular interest.