ANALOGOUS OF CONVERSE PALEY-WIENER THEOREM
IN THE CONTEXT OF POSITIVE DEFINITE KERNEL
Osmin Ferrer1, Arnaldo de la Barrera2,
Jorge Rodriguez3
1 Department of Mathematics, University of Sucre
Sincelejo - 700001, COLOMBIA
2 Department of Mathematics, University of Pamplona
Pamplona - 543050, COLOMBIA
3 Department of Mathematics
University of Atlantico - University of Norte
Barranquilla - 08002, COLOMBIA

Abstract

We formulate and prove an analogous of converse Paley-Wiener theorem in the context of positive definite kernel. The main ingredient in the proof is Kolmogorov decomposition. Finally, some applications to stochastic processes are given.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 1
Year: 2021

DOI: 10.12732/ijam.v34i1.7

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] D.E. Evans and J.T. Lewis, Dilations of Irreversible Evolutions in Algebraic Quantum Theory, Communications of the Dublin Institute for Advanced Studies, Ser. A: Theoretical Physics, Vol. 24 (1977).
  2. [2] R. Bruzual, A. De la Barrera and M. Dom´ınguez, On positive definite kernels, related problems and applications, Extracta Math., 29, No 1-2 (2014), 97-115.
  3. [3] R.J. Duffin and J.J. Eachus, Some notes on an expansion theorem of Paley and Wiener, Bull. Amer. Math. Soc., 48, No 12 (1942), 850-855.
  4. [4] R. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Reprint of the 1934 original, Amer. Math. Soc. Colloquium Publications, 19. Amer. Math. Soc., Providence, RI (1987).
  5. [5] R.M. Young, An Introduction to Nonharmonic Fourier Series, Pure and Applied Mathematics, Vol. 93, Academic Press, Inc. [Harcourt Brace Jovanovich, Publ.], New York-London (1980).
  6. [6] T. Constantinescu, Schur Parameters, Factorization and Dilation Problems, Operator Theory: Advances and Applications, 82, Birkhauser Verlag, Basel (1996).