On the Existence of Generalized Pólya Frequency Functions Corresponding to Entire Functions with Zeros in Angular Sectors Generalized Pólya Frequency Functions

نویسندگان

  • ANDREW BAKAN
  • STEPHAN RUSCHEWEYH
چکیده

Generalized Pólya frequency functions are introduced through inverse Mellin transformations of the reciprocals of real entire functions with all zeros in sectors A and −Aφ for 0 ≤ φ ≤ π4 , where A := {z ∈ C | | arg z| ≤ φ}. It is shown that the constant π4 is best possible in this context.

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تاریخ انتشار 2011