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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    $\begingroup$ Why does this have a "banach algebras tag", given that Gelfand's work lies 25-30 years in the future? $\endgroup$ – Yemon Choi Sep 11 '17 at 5:29

this 2014 overview lists the known translations in English of Hilbert's books, the 1912 book in the OP is not among them:

  • $\begingroup$ 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. $\endgroup$ – Colin McLarty Sep 11 '17 at 19:11
  • $\begingroup$ @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 $\endgroup$ – Carlo Beenakker Sep 11 '17 at 20:22

Yes, there is a translation, but not an official one and only of the "Erste Mitteilung", not the whole book: The pdf

FREDHOLM, HILBERT, SCHMIDT Three Fundamental Papers on Integral Equations, Translated with commentary by G. W. Stewart

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."

  • $\begingroup$ great find --- this translation is only of the first of the six chapters of Hilbert's 1912 book, am I correct? $\endgroup$ – Carlo Beenakker Sep 12 '17 at 10:37
  • $\begingroup$ Yes, it's only the "Erste Mitteilung". $\endgroup$ – Dirk Sep 13 '17 at 6:36
  • $\begingroup$ Excellent find - thank you so much Dirk !! $\endgroup$ – Andre Sep 13 '17 at 11:26

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