# Alexandre Eremenko

 10,552 Reputation 4371 views

## Registered User

 Name Alexandre Eremenko Member for 9 months Seen yesterday Website Location United States Age 58
Math Professor
 1d comment Triangle area on surfaces of constant curvatureAnton, sorry I looked at 119953 and I don't understand your objection. In elementary geometry we deal with areas of polygons. The area is defined by a) finite additivity, b) monotonicity, invariance with respect to motion, c) the area of the unit square is 1. From this it is easy to derive that the area of a polygon exists and is unique. And I believe Euclid did it rigorously. Kiselev (who wrote the common Russian high school geometry text) did it rigorously, and I studied this in 8-th grade. What's wrong with all this? 2d awarded ● Necromancer May14 comment Convergence at the radius of convergenceThis is by Abel's theorem. May14 comment Triangle area on surfaces of constant curvatureSorry, I was using Russian edition, where this is called Chapter V. Now I checked the original, and in the original it is VOLUME V. And unfortnately I did not find an English translation:-( May14 revised Triangle area on surfaces of constant curvatureadded 903 characters in body May14 comment Triangle area on surfaces of constant curvatureAnton: I disagree with what you say. The area of a TRIANGLE is an elementary notion. (The theory of areas of triangles in Euclid is completely rigorous, by all modern standards.) And the formula has a really elementary proof. May14 revised Triangle area on surfaces of constant curvatureadded 2 characters in body; added 1 characters in body May13 accepted Triangle area on surfaces of constant curvature May12 answered Triangle area on surfaces of constant curvature May10 answered Jordan curve theorem: Can every point on the curve be reached from each region? May6 answered Closed form solution to an iterative equation. May4 answered Classic applications of Baire category theorem May2 answered Asymptotic series Apr29 asked Univalent functions with non-negative coefficients Apr29 answered Good book on Calculus of Variations Apr28 accepted Mathematical Paper That Just Links Two Different Fields of Sciences Apr27 revised Relation of degree and genus of superelliptic curvesadded 891 characters in body Apr26 comment Relation of degree and genus of superelliptic curvesI will explain if you vote up my answer:-) Apr25 accepted Relation of degree and genus of superelliptic curves Apr24 answered Relation of degree and genus of superelliptic curves Apr20 comment Growth of the reciprocal gamma function in the critical stripAnd in general, Stirling formula (asymptotic expansion) holds as $|z|\to\infty$ uniformly with respect to $\arg z$ in every angle of the form $|\arg z|<\pi-\epsilon,\; \epsilon>0$. Apr20 accepted Newton integration without integration Apr19 accepted Monodromy of "complex Schwarz-Christoffel maps Apr19 answered Monodromy of "complex Schwarz-Christoffel maps Apr19 revised Great mathematics books by pre-modern authorsadded 40 characters in body Apr19 revised Great mathematics books by pre-modern authorsadded 384 characters in body Apr19 answered Great mathematics books by pre-modern authors Apr19 comment A question from complex analysisThis is a reasonable question, especially now, when it is corrected. Please don't close it. Apr19 accepted Representation of all pass transfer functions/inner functions as Blaschke product. Apr19 comment A question from complex analysisOf course one can easily modify the statement to eliminate these simple counterexamples but I leave this to the author. Apr18 answered A question from complex analysis Apr18 comment Newton integration without integrationMedvedev is an historian, not a real mathematician, so it is possible that he confused something. The book on the history of integral that I have (by I. Pesin, who is a mathematician) does not mention this paper of Lebesgue. But of course I can say nothing definite without seeing Medvedev's book. Apr18 comment Newton integration without integrationInteresting. Unfortunately I do not have Medvedev's book, and on the Internet I found it for $229, and my interest 8is not sufficient to pay this amount to satisfy it:-( Apr18 answered Representation of all pass transfer functions/inner functions as Blaschke product. Apr18 comment Is rigour just a ritual that most mathematicians wish to get rid of if they could? On my opinion, this is a legitimate and important question. These discussions are common, and sometimes even happen on the pages of BAMS. I propose to reopen. Apr18 comment Newton integration without integrationWhat about Medvedev? Does he say anything about this paper of Lebesgue? Apr17 answered Weierstrass factorization with$L^2$estimates? Apr17 comment Newton integration without integrationAntonio, In this procedure you only need that integrals of uniformly convergent functions are convergent. Apr16 answered textbooks on asymptotic expansions Apr16 revised Newton integration without integrationadded 107 characters in body Apr16 answered Newton integration without integration Apr16 comment Spectral densities and their corresponding covariance functions.Your first formula for$S_X$is incorrect:$C_X$is even but$\exp(-i\omega t)$is not, so the integrand is not even. The second formula (with$\cos\$) is correct. Apr15 comment Solution of an infinite differential systemjoaopa: You should vote my answer up if you want me to answer further questions:-) Apr15 answered Solution of an infinite differential system Apr12 revised Mean value theorem for harmonic functions on ellipsoidadded 198 characters in body Apr12 comment Is there a deep reason for the fecundity of involutions?Ketil: I did not understand your remark: 1) You did not like my answer because you think it is wrong, or for some other reason? 2) About the hammer: if we "understand well" something, does not this indicate that this thing EXISTS in the outside world ? Apr12 revised Is there a deep reason for the fecundity of involutions?added 43 characters in body Apr12 comment Is there a deep reason for the fecundity of involutions?Carlo: Thanks! Very interesting detail:-) Apr12 comment A graduate course on Sturm Liouville theory?Yes, and Atkinson's book is good for this. It has more algebraic flavor on my opinion, because he considers discrete and continuous problems together. Same applies to Krein-Gantmakher book. Apr12 comment Mean value theorem for harmonic functions on ellipsoidR.W.: I mentioned that one can do without. With centrality condition you can take the averages over all surfaces similar to the given surface and having center at x, to recover u(x). Without centrality, we have to restrict ourselves to shifts and homotheties of the given surface.