bio  website  math.purdue.edu/~eremenko 

location  United States  
age  60  
visits  member for  2 years, 4 months 
seen  10 hours ago  
stats  profile views  8,193 
Math Professor
22h

answered  Not especially famous, longopen problems which anyone can understand 
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awarded  Nice Answer 
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comment 
Roots in the solution
Instead of Googling, take some good book (Birkhof and Rota, or Coddington Levinson, or Ince). 
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awarded  Nice Answer 
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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? 
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awarded  Necromancer 
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revised 
Conformal map of polygon with circle segments
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revised 
Not especially famous, longopen problems which anyone can understand
added 21 characters in body 
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answered  Not especially famous, longopen problems which anyone can understand 
2d

revised 
Entire function bounded at every line
added 317 characters in body 
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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. 
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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). 
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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. 
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Conformal map of polygon with circle segments
@user213437: if you state your problem precisely, perhaps I can give a more specific reference. 
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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. 
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revised 
Entire function bounded at every line
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answered  Entire function bounded at every line 
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revised 
Conformal map of polygon with circle segments
added 369 characters in body 
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answered  Conformal map of polygon with circle segments 
Dec 14 
answered  Planar curves identical to their inverses 