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Is there any Russian-authored textbook on Analysis equivalent to Big Rudin (Real and Complex Analysis)?

I like Russian math textbooks a lot. I am looking for Russian textbooks (either in English or Russian, preferably English) in analysis covering the same material as "Principles of Mathematical Analysis", "Real and Complex Analysis" and "Functional Analysis" by Rudin.

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    $\begingroup$ A standard introductory analysis book used by Russian students at universities today is Zorich's "Mathematical Analysis," which has been published by Springer-Verlag as a two-volume set in English, called "Mathematical Analysis I" and "Mathematical Analysis II". $\endgroup$
    – KConrad
    Commented Sep 21, 2017 at 21:25
  • $\begingroup$ Am I the only one who thinks it somewhat strange to ask for English language textbooks authored by people of a selected nationality? $\endgroup$
    – Michael Greinecker
    Commented Sep 22, 2017 at 7:04
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    $\begingroup$ @MichaelGreinecker -- I guess the idea here is that there is something like a "Russian school of mathematics", which influences the way a text book is written and is not lost in translation. $\endgroup$
    – Carlo Beenakker
    Commented Sep 22, 2017 at 7:18

6 Answers 6

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A classic is Kolmogorov and Fomin's Elements of the Theory of Functions and Functional Analysis, also published (in a revised version) under the title Introductory Real Analysis. (Amazon presents them as distinct books, but they are really based on the same Russian text.) From a somewhat less distinguished author there is also G.E. Shilov, Elementary Real and Complex Analysis.

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    $\begingroup$ "From a somewhat less distinguished author there is also G.E. Shilov..." Well, every Russian author who is not Kolmogorov is somewhat less distinguished... $\endgroup$
    – Pete L. Clark
    Commented Sep 21, 2017 at 19:06
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    $\begingroup$ Yes, that was a very clearly written textbook. $\endgroup$
    – Michael
    Commented Sep 21, 2017 at 20:06
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    $\begingroup$ @PeteL.Clark -- that seems to be too strong a statement. $\endgroup$
    – Suvrit
    Commented Sep 22, 2017 at 0:37
  • $\begingroup$ Thanks,Beenakker. I think Kolmogorov,Shilov's cover same material as Rudin's Principles of Mathematical Analysis. Can you suggest one which covers Real & Complex Analysis? $\endgroup$
    – Kumar
    Commented Sep 22, 2017 at 6:12
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    $\begingroup$ @Suvrit (That "thank you very much" wasn't directed at you, and is actually hard to explain because it's all in how you say it. It's almost like a wink of the eye, and definitely with a smile.) $\endgroup$
    – Todd Trimble
    Commented Sep 22, 2017 at 20:56
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My teachers suggested Real Analysis: Measures, Integrals and Applications by Makarov and Podkorytov and Lectures And Exercises on Functional Analysis by Helemskii when I had those courses. There is a 2nd edition of Helemskii available in russian.

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I can highly recommend Grigorii M. Fichtenholz's books, they are very instructive for students.

I am not sure about the English title or Russian Original Title, the German versions are called
Differential- und Integralrechnung. I,II,III.

This is a classical textbook. The topics are more basic (series, integration....), not covering the functional analysis of Rudin.

See this link in MathSciNet for some of his books: http://www.ams.org/mathscinet-getitem?mr=84531

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    $\begingroup$ This book was outdated 80 years ago. $\endgroup$
    – Misha
    Commented Sep 22, 2017 at 1:09
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There is no Russian equivalent of these books, like there is no equivalent of "baby Rudin" (which they translated). But one can certainly cover the same material with several books available in Russian (some of them translated into Russian). Some of these books are mentioned in other answers.

EDIT. I suspect that absence of equivalent books is due to the difference of education systems. Undergraduate education in Soviet Union was much more advanced then undergraduate education in the US. For example Kolmogorov-Fomin, and Shilov, and Helemski mentioned in the other answers are undergraduate textbooks. (Normally such courses of Complex and Functional analysis are taught on the 3-d year of undergraduate studies). A student who completed undergraduate education and enrolled to a graduate pprogram is expected to begin his/her research immediately.

So there is no such thing as a "graduate text in Complex Analysis" in Russian. Graduate education will be much more focused (on some particular topic in Complex Analysis), and the student will be expected to read original papers and monographs, rather than a textbook.

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  • $\begingroup$ Translated into English, you mean? $\endgroup$
    – Fedor Petrov
    Commented Sep 21, 2017 at 20:29
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    $\begingroup$ Translated into Russian. The question was "what is available in Russian?" This is how I understood the question. $\endgroup$
    – Alexandre Eremenko
    Commented Sep 22, 2017 at 1:12
  • $\begingroup$ I am looking for Russian-authored books translated into English $\endgroup$
    – Kumar
    Commented Sep 22, 2017 at 6:03
  • $\begingroup$ @Kumar: What for? Why do you care about the native language of the book author? $\endgroup$
    – Alexandre Eremenko
    Commented Sep 22, 2017 at 12:48
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    $\begingroup$ @AlexandreEremenko I suspect that the OP is associating a certain style of writing with "Russian math textbooks". If I had to guess, it would be a style which emphasizes lots of intuition and doesn't adhere strictly to a drier "definition-theorem-proof" format such as found in Rudin's books. But this is only a guess. $\endgroup$
    – Todd Trimble
    Commented Sep 22, 2017 at 19:56
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A good choice he would be the two-volume textbook of Vladimir Zorich: Mathematical Analysis which is available in English now in its second edition. See http://www.springer.com/gp/book/9783662487907 and http://www.springer.com/gp/book/9783662489918 . The books are available in German, too.

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    $\begingroup$ It is what Kconrad said in the comment below the answer. $\endgroup$
    – A_S
    Commented Sep 22, 2017 at 7:02
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Functional analysis: S. S. Kutateladze Fundamentals of Functional Analysis

Complex analysis: Yu. V. Sidorov, M. V. Fedoryuk, M. I. Shabunin Lectures On The Theory Of Functions Of A Complex Variable

Elements of Fourier analysis: N. I. Akhiezer Lectures on Integral Transforms

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