23,266 reputation
263120
bio website math.purdue.edu/~eremenko
location United States
age 60
visits member for 2 years, 4 months
seen 10 hours ago
Math Professor

22h
answered Not especially famous, long-open problems which anyone can understand
1d
awarded  Nice Answer
1d
comment Roots in the solution
Instead of Googling, take some good book (Birkhof and Rota, or Coddington Levinson, or Ince).
1d
awarded  Nice Answer
1d
comment Roots in the solution
Sturm's theorem says that $n$-th eigenfunction has $n$ roots ON THE INTERVAL where the operator acts. If it happens to be a polynomial, this polynomial must have $n$ roots only on this interval. What else are you asking?
1d
awarded  Necromancer
1d
revised Conformal map of polygon with circle segments
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2d
revised Not especially famous, long-open problems which anyone can understand
added 21 characters in body
2d
answered Not especially famous, long-open problems which anyone can understand
2d
revised Entire function bounded at every line
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2d
comment Entire function bounded at every line
The question was not about entire functions tending to zero on EVERY line, but such functions are also traditionally (since approx 1900) constructed by the general method I described.
2d
comment Conformal map of polygon with circle segments
@user2133437: in this picture two sides (not one) are arcs of circles. The only specific is that two angles are 90 degrees. You may look at my paper arXiv:1111.2296 where a similar quadrilateral is mapped (in the end of the paper).
2d
comment Conformal map of polygon with circle segments
@user213437: yes, the condition all sides but one are straight may give some simplification. It will help if you state your problem more precisely: what are the angles, and what do you want to know about the mapping.
2d
comment Conformal map of polygon with circle segments
@user213437: if you state your problem precisely, perhaps I can give a more specific reference.
2d
comment Conformal map of polygon with circle segments
@user213437: the literature on conformal maps of quadrilaterals is enormous. I am not familiar with that particular book you refer to, but I suppose that it contains some standard material on this.
2d
revised Entire function bounded at every line
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2d
answered Entire function bounded at every line
2d
revised Conformal map of polygon with circle segments
added 369 characters in body
2d
answered Conformal map of polygon with circle segments
Dec
14
answered Planar curves identical to their inverses