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Complex Variable Positive Definite Functions

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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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References

  1. Aronszajn, N.: Theory of reproducing kernels. Trans. Am. Math. Soc. 68, 337–404 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berg, C., Christensen, J., Ressel, P.: Harmonic Analysis on Semigroups, GTM 100 edn. Springer-Verlag, New York (1984)

    Book  MATH  Google Scholar 

  3. Bisgaard, T., Sasvári, Z.: Characteristic Functions and Moment Sequences. Nova Science Publishing, New York (2000)

    MATH  Google Scholar 

  4. Buescu, J., Paixão, A.: Positive definite matrices and differentiable reproducing kernel inequalities. J. Math. Anal. Appl. 320, 279–292 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Buescu, J., Paixão, A.: Eigenvalue distribution of positive definite kernels on unbounded domains. Integral Equ. Oper. Theory 57(1), 19–41 (2007)

    Article  MATH  Google Scholar 

  6. Buescu, J., Paixão, A.: A linear algebraic approach to holomorphic reproducing kernels in \({\mathbb{C}}^n\). Linear Algebra Appl. 412(2–3), 270–290 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Buescu, J., Paixão, A.: Positive definite matrices and integral equations on unbounded domains. Differ. Integral Equ. 19(2), 189–210 (2006)

    MATH  Google Scholar 

  8. Buescu, J., Paixão, A.: On differentiability and analyticity of positive definite functions. J. Math. Anal. Appl. 375(1), 336–341 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Devinatz, A.: On infinitely differentiable positive definite functions. Proc. Am. Math. Soc. 8, 3–10 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dugué, D.: Analyticité et convexité des fonctions caractéristiques. Annales de l’I. H. P. 12(1), 45–56 (1951)

    MATH  Google Scholar 

  11. Kosaki, H.: Positive definiteness of functions with applications to operator norm inequalities. Mem. Am. Math. Soc., 212 (2011)

  12. Lukacs, E., Szasz, O.: On analytic characteristic functions. Pac. J. Math. 3, 615–625 (1953)

    Google Scholar 

  13. Moore, E.H.: General analysis. Mem. Am. Philos. Soc., Part I (1935), Part II (1939)

  14. Sasvári, Z.: Positive definite and definitizable functions. In: Mathematical Topics, vol. 2. Akademie Verlag, Berlin (1994)

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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.

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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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