scholarly journals Extremal problems for Lorentz classes of nonnegative polynomials in $L^2$ metric with Jacobi weight

1988 ◽  
Vol 102 (2) ◽  
pp. 283-283
Author(s):  
Gradimir V. Milovanovi{ć ◽  
Miodrag S. Petkovi{ć
Keyword(s):  
Extremal Problems ◽  
Nonnegative Polynomials ◽  
Jacobi Weight

Some extremal problems for circular polygons

1996 ◽  
Vol 80 (4) ◽  
pp. 1956-1961
Author(s):  
A. Yu. Solynin
Keyword(s):  
Extremal Problems

Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight

2017 ◽  
Vol 06 (01) ◽  
pp. 1750003
Author(s):  
Shulin Lyu ◽  
Yang Chen
Keyword(s):  
Asymptotic Expansions ◽  
Hankel Determinant ◽  
Generalized Jacobi Weight ◽  
Jacobi Weight ◽  
Special Cases ◽  
Painlevé Vi Equation

We consider the generalized Jacobi weight [Formula: see text], [Formula: see text]. As is shown in [D. Dai and L. Zhang, Painlevé VI and Henkel determinants for the generalized Jocobi weight, J. Phys. A: Math. Theor. 43 (2010), Article ID:055207, 14pp.], the corresponding Hankel determinant is the [Formula: see text]-function of a particular Painlevé VI. We present all the possible asymptotic expansions of the solution of the Painlevé VI equation near [Formula: see text] and [Formula: see text] for generic [Formula: see text]. For four special cases of [Formula: see text] which are related to the dimension of the Hankel determinant, we can find the exceptional solutions of the Painlevé VI equation according to the results of [A. Eremenko, A. Gabrielov and A. Hinkkanen, Exceptional solutions to the Painlevé VI equation, preprint (2016), arXiv:1602.04694 ], and thus give another characterization of the Hankel determinant.

Some extremal problems on classes of summable functions

1972 ◽  
Vol 24 (5) ◽  
pp. 574-578
Author(s):  
L. G. Khomutenko
Keyword(s):  
Extremal Problems
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