Alexandre Eremenko

10,552
Reputation
4371 views
Is this your account?

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 curvature
Anton, 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
May
14
 comment Convergence at the radius of convergence
This is by Abel's theorem.
May
14
 comment Triangle area on surfaces of constant curvature
Sorry, 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:-(
May
14
 revised Triangle area on surfaces of constant curvature
added 903 characters in body
May
14
 comment Triangle area on surfaces of constant curvature
Anton: 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.
May
14
 revised Triangle area on surfaces of constant curvature
added 2 characters in body; added 1 characters in body
May
13
 accepted Triangle area on surfaces of constant curvature
May
12
 answered Triangle area on surfaces of constant curvature
May
10
 answered Jordan curve theorem: Can every point on the curve be reached from each region?
May
6
 answered Closed form solution to an iterative equation.
May
4
 answered Classic applications of Baire category theorem
May
2
 answered Asymptotic series
Apr
29
 asked Univalent functions with non-negative coefficients
Apr
29
 answered Good book on Calculus of Variations
Apr
28
 accepted Mathematical Paper That Just Links Two Different Fields of Sciences
Apr
27
 revised Relation of degree and genus of superelliptic curves
added 891 characters in body
Apr
26
 comment Relation of degree and genus of superelliptic curves
I will explain if you vote up my answer:-)
Apr
25
 accepted Relation of degree and genus of superelliptic curves
Apr
24
 answered Relation of degree and genus of superelliptic curves
Apr
20
 comment Growth of the reciprocal gamma function in the critical strip
And in general, Stirling formula (asymptotic expansion) holds as $|z|\to\infty$ uniformly with respect to $\arg z$ in every angle of the form $|\arg z|<\pi-\epsilon,\; \epsilon>0$.
Apr
20
 accepted Newton integration without integration
Apr
19
 accepted Monodromy of "complex Schwarz-Christoffel maps
Apr
19
 answered Monodromy of "complex Schwarz-Christoffel maps
Apr
19
 revised Great mathematics books by pre-modern authors
added 40 characters in body
Apr
19
 revised Great mathematics books by pre-modern authors
added 384 characters in body
Apr
19
 answered Great mathematics books by pre-modern authors
Apr
19
 comment A question from complex analysis
This is a reasonable question, especially now, when it is corrected. Please don't close it.
Apr
19
 accepted Representation of all pass transfer functions/inner functions as Blaschke product.
Apr
19
 comment A question from complex analysis
Of course one can easily modify the statement to eliminate these simple counterexamples but I leave this to the author.
Apr
18
 answered A question from complex analysis
Apr
18
 comment Newton integration without integration
Medvedev 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.
Apr
18
 comment Newton integration without integration
Interesting. 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:-(
Apr
18
 answered Representation of all pass transfer functions/inner functions as Blaschke product.
Apr
18
 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.
Apr
18
 comment Newton integration without integration
What about Medvedev? Does he say anything about this paper of Lebesgue?
Apr
17
 answered Weierstrass factorization with $L^2$ estimates?
Apr
17
 comment Newton integration without integration
Antonio, In this procedure you only need that integrals of uniformly convergent functions are convergent.
Apr
16
 answered textbooks on asymptotic expansions
Apr
16
 revised Newton integration without integration
added 107 characters in body
Apr
16
 answered Newton integration without integration
Apr
16
 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.
Apr
15
 comment Solution of an infinite differential system
joaopa: You should vote my answer up if you want me to answer further questions:-)
Apr
15
 answered Solution of an infinite differential system
Apr
12
 revised Mean value theorem for harmonic functions on ellipsoid
added 198 characters in body
Apr
12
 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 ?
Apr
12
 revised Is there a deep reason for the fecundity of involutions?
added 43 characters in body
Apr
12
 comment Is there a deep reason for the fecundity of involutions?
Carlo: Thanks! Very interesting detail:-)
Apr
12
 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.
Apr
12
 comment Mean value theorem for harmonic functions on ellipsoid
R.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.