Positivity

, Volume 22, Issue 1, pp 341–356 | Cite as

Weinstein positive definite functions

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Abstract

In this paper, we introduce the notion of the Weinstein positive definite functions and we state a version of Bochner’s theorem. Furthermore, we study the strictly Weinstein positive definite functions and we present a sufficient condition for a function to be strictly Weinstein positive definite.

Keywords

Positive definite functions Weinstein positive definite functions Strictly Weinstein positive definite functions Bochner theorem 

Mathematics Subject Classification

42B10 44A15 42A82 

References

  1. 1.
    Bateman, H.: Tables of Integral Transforms, 1st edn. McGraw-Hill, NewYork (1954)Google Scholar
  2. 2.
    Ben Nahia, Z., Ben Salem, N.: On a mean value property associated with the Weinstein operator. In: Krl, J. et al. (eds.) Potential Theory Proceedings-ICPT 94, pp. 243–253 (1996)Google Scholar
  3. 3.
    Ben Nahia, Z., Ben Salem, N.: Spherical harmonics and applications associated with the Weinstein operator. In: Král, J. et al. (eds) Potential Theory Proceedings-ICPT 94 . ICPT 94, pp. 235–241 (1996)Google Scholar
  4. 4.
    Brelot, M.: Equation de Weinstein et potentiels de Marcel Riesz. Seminaire de Theorie de Potentiel Paris, No. 3. Lect. Notes Math. 681, 18–38 (1978)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chettaoui, C., Triméche, K.: Bochner–Hecke theorems for the Weinstein transform and application. Fract. Calc. Appl. Anal. 13(3), 261–280 (2010)Google Scholar
  6. 6.
    Debnath, L.: Integral Transform and Their Applications. CRC Press, Boca Raton (1995)MATHGoogle Scholar
  7. 7.
    Mehrez, K.: Paley–Wiener theorem for the Weinstein transform and applications. Integral Trans. Spec. Funct 28(8), 616–628 (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Département de Mathématiques ISSAT KasserineUniversité de KairouanKasserineTunisia
  2. 2.Département de Mathématiques, Faculté de Sciences de TunisUniversité Tunis El ManarTunisTunisia

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