Does anyone know if there is an English translation of Hilbert's: "Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen, Teubner, Leipzig, 1912". ??
Thanks, Andre
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2$\begingroup$ Why does this have a "banach algebras tag", given that Gelfand's work lies 25-30 years in the future? $\endgroup$– Yemon ChoiCommented Sep 11, 2017 at 5:29
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2 Answers
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Yes, there is a translation, but not an official one and only of the "Erste Mitteilung", not the whole book: The pdf
contains "Foundations of a General Theory of Linear Integral Equations" (starting on p.55 (59 in the pdf)). This is a translation of the paper
Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Erste Mitteilung Nachrichten der Wissenschaftlichen Gesellschaft zu Göttingen, Math.-phys. Kl. (1904),49-91".
I haven't seen translation of the five other "Mitteilung" under the same title (but I haven't seen version of the second, third and sixth Mitteilung even in German…).
The other two papers in the pdf are Fredholm's "On a Class of Functional Equations" and Schmidt's "On the Theory of Linear and Nonlinear Integral Equations. Part I: The Expansion of Arbitrary Functions by Prescribed Systems."
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$\begingroup$ great find --- this translation is only of the first of the six chapters of Hilbert's 1912 book, am I correct? $\endgroup$ Commented Sep 12, 2017 at 10:37
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$\begingroup$ Yes, it's only the "Erste Mitteilung". $\endgroup$– DirkCommented Sep 13, 2017 at 6:36
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$\begingroup$ Excellent find - thank you so much Dirk !! $\endgroup$– AndreCommented Sep 13, 2017 at 11:26
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this 2014 overview lists the known translations in English of Hilbert's books, the 1912 book in the OP is not among them:
- Grundlagen der Geometrie (1899) -- The Foundations of Geometry (1902)
- Methoden der Mathematischen Physik, Vol. I (1924) and Vol. II (1937) -- Methods of Mathematical Physics, Vol. I (1953) and Vol. II (1962)
- Grundzüge der theoretischen Logik (1928) -- Principles of Mathematical Logic (1950)
- Anschauliche Geometrie (1932) -- Geometry and the Imagination (1952)
- Hilbert's invariant theory papers (1978) [four papers: On the invariant properties of special binary forms, especially spherical functions. On a general point of view for invariant-theoretic investigation of binary forms. On the theory of algebraic forms. On the complete systems of invariants.]
- Vorlesungen über algebraische Invariantentheorie (1897) -- Lecture notes on the Theory of algebraic invariants (1993)
- Theorie der algebraischen Zahlkörper (1897) -- The theory of algebraic number fields (1998)
answered Sep 11, 2017 at 6:25
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$\begingroup$ But it is worth mentioning that the same source does refer to (and quote in full) an English language review of the work, by Thomas Haken Grönwall. Bull. Amer. Math. Soc. 20 (1914), 326. $\endgroup$ Commented Sep 11, 2017 at 19:11
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$\begingroup$ @ColinMcLarty --- thanks, but I'm afraid that review will not be very helpful, it's just a one-paragraph summary: projecteuclid.org/download/pdf_1/euclid.bams/1183422669 $\endgroup$ Commented Sep 11, 2017 at 20:22