Complex Variable Positive Definite Functions

Abstract

In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions.

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Acknowledgments

The first author acknowledges partial support by Fundação para a Ciência e Tecnologia, PEst-OE/MAT/UI0209/2011.

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Correspondence to Jorge Buescu.

Additional information

Communicated by Saburou Saitoh.

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Buescu, J., Paixão, A.C. Complex Variable Positive Definite Functions. Complex Anal. Oper. Theory 8, 937–954 (2014). https://doi.org/10.1007/s11785-013-0319-1

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Keywords

  • Positive definite functions
  • Complex analysis
  • Meromorphic functions

Mathematics Subject Classification (1991)

  • Primary 42A82
  • Secondary 30A10
  • 30C40