On the location of the singularities of the function generated by the Bergman operator of the second kind

Rosenthal, Paul

doi:10.1090/S0002-9939-1974-0328293-4

On the location of the singularities of the function generated by the Bergman operator of the second kind
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Proc. Amer. Math. Soc. 44 (1974), 157-162 Request permission

Abstract:

Let $g(x,y) = {P_2}(f)$ be Bergman’s operator of the second kind, $f(q)$ analytic at $q = 0$. The purpose of this paper is to generalize a previous result of the author on the location of the singularities of $g(x,y)$ when $f(q)$ had only a simple pole. $f(q)$ now is assumed to be a rational function whose poles are distributed along the arc of a circle. An order relation is also obtained for $g(x,y)$ for certain fixed $x$ and $y$ sufficiently large and positive.

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