High degree simple partial fractions in the Bergman space: Approximation and Optimization

We consider the class of standard weighted Bergman spaces Aα2(D) and the set SFN(T) of simple partial fractions of degree N with poles on the unit circle. We prove that under certain conditions, the simple partial fractions of order N, with n poles on the unit circle attain minimal norm if and only...

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Vydáno v:Analysis and mathematical physics Ročník 16; číslo 1; s. 2
Hlavní autor: Biehler, Nikiforos
Médium: Journal Article
Jazyk:angličtina
Vydáno: Heidelberg Springer Nature B.V 01.02.2026
Témata:
Approximation
Mathematical functions
Poles
Polynomials
ISSN:1664-2368, 1664-235X
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Shrnutí:We consider the class of standard weighted Bergman spaces Aα2(D) and the set SFN(T) of simple partial fractions of degree N with poles on the unit circle. We prove that under certain conditions, the simple partial fractions of order N, with n poles on the unit circle attain minimal norm if and only if the points are equidistributed on the unit circle. We show that this is not the case if the conditions we impose are not met, exhibiting a new interesting phenomenon. We find sharp asymptotics for these norms. Additionally we describe the closure of these fractions in the standard weighted Bergman spaces.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-025-01145-8