Skip to main content
Log in

Positive Definite Functions as an Instrument of Mathematical Analysis

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

For the subject in question, the paper describes its connections that are close to the author’s interests with branches of functional analysis. The present survey may be suitable as a basis for a special course.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. M. Boas, Jr. and A. C. Schaffer, “Variational method in entire functions,” Am. J. Math., 79, No. 4, 857–884 (1957).

    Article  MATH  Google Scholar 

  2. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin (1973).

    Book  MATH  Google Scholar 

  3. N. Bourbaki, Élémentes de mathématique. Variétés différentielles et analytiques. Fascicule de résultats, Hermann, Paris (1967).

  4. H. Davenport, Multiplicative Number Theory, Chicago, Markham (1968).

    Google Scholar 

  5. E. A. Gorin, “On the research of G. E. Shilov in the theory of commutative Banach algebras and its subsequent development,” Russ. Math. Surv., 33, 193–217 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  6. E. A. Gorin, “Bernstein’s inequality from the point of view of operator theory,” Selecta Math. Sov., 7, No. 3, 191–219 (1988).

    MATH  Google Scholar 

  7. E. A. Gorin, “A generalization of a theorem of Fuglede,” Algebra Anal., 5, No. 4, 83–97 (1993).

    MATH  MathSciNet  Google Scholar 

  8. E. A. Gorin, “Universal symbols on locally compact Abelian groups,” Bull. Pol. Acad. Sci., 51, No. 2, 199–204 (2003).

    MATH  MathSciNet  Google Scholar 

  9. E. A. Gorin, “Estimates for the involution of decomposable elements of a complex Banach algebra,” Func. Anal. Appl., 39, No. 4, 14–31 (2005).

    Article  MathSciNet  Google Scholar 

  10. E. A. Gorin, “Asymptotic law for the distribution of prime numbers in the context of free Abelian semigroups,” Russ. J. Math. Phys., 13, No. 1, 31–54 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  11. E. A. Gorin, “Fragments of the research biography of D. A. Raikov: harmonic analysis,” Russ. Math. Surv., 61, No. 5, 955–969 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  12. E. A. Gorin, “The Möbius function on Abelian semigroups,” Funct. Anal. Appl., 45, No. 1, 73–76 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  13. E. A. Gorin and S. Norvidas, “Universal symbols on locally compact Abelian groups”, Funct. Anal. Appl., 47, No. 1, 1–13 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Isidro and L. Stachò, Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction, North-Holland, Amsterdam (1984).

    Google Scholar 

  15. W. Kaup, “Bounded symmetric domains and generalized operator algebras,” in: Real Analysis and Functional Analysis Joint Symposium (2007), pp. 45–56.

  16. Yu. I. Lyubich, V. I. Matsaev, and G. M. Feldman, “On representations with a separable spectrum,” Funct. Anal. Appl., 7, No. 2, 129–136 (1973).

    Article  MATH  Google Scholar 

  17. B. Sz.-Nagy, Ch. Foias, Analyse harmonique des opérateurs de l’espace de Hilbert, Akad. Kaidó, Budapest (1967).

  18. S. Norvidas, “On stability of differential operators in spaces of entire functions,” Dokl. Akad. Nauk SSSR, 291, No. 3, 548–551 (1986).

    MathSciNet  Google Scholar 

  19. S. Norvidas, “Functional calculus of Hermitian elements and Bernstein inequalities,” Funct. Anal. Appl., 40, No. 2, 148–150 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  20. A. G. Postnikov, Introduction to Analytic Number Theory, Amer. Math. Soc., Providence (1988).

    MATH  Google Scholar 

  21. B. Riemann, Gesammelte mathematische Werke und wissenschaftlicher Nachlass, Teubner, Leipzig (1892).

    MATH  Google Scholar 

  22. W. Rudin, Fourier Analysis on Groups, Interscience Publishers, New York (1967).

    Google Scholar 

  23. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford (1951).

    MATH  Google Scholar 

  24. H. Upmeier, Symmetric Banach Manifolds and Jordan C*-Algebras, North-Holland, Amsterdam (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. A. Gorin.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 7, pp. 67–95, 2011/12.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gorin, E.A. Positive Definite Functions as an Instrument of Mathematical Analysis. J Math Sci 197, 492–511 (2014). https://doi.org/10.1007/s10958-014-1730-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-1730-5

Keywords

Navigation