Skip to main content

Symbolic Calculus Applied to Convex Functions and Associated Diffusions

  • Chapter
Deformations of Mathematical Structures
  • 225 Accesses

Abstract

We prove classical inequalities for generalized second-order differential operators in order to study some potential theoretic properties of convex functions and associated diffusions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BEDFORD, E. and M. KALKA: ‘Foliations and complex Monge-Ampere equations’, Comm. Pure Appl. Math. 30 (1977), 543–570.

    Article  MathSciNet  MATH  Google Scholar 

  2. BEDFORD, E. and B.A. TAYLOR: ‘Variational properties of the complex Monge-Ampère equation II. Intrinsic norm’, Amer, J. Math. 101 (1979), 1131–1166.

    Article  MathSciNet  MATH  Google Scholar 

  3. CEGRELL, U.: ‘On the domains of existence for plurisubharmonic functions’, Banach Center Publications 11 (1983), 33–37.

    MathSciNet  Google Scholar 

  4. DYNKIN, E.B.: Markov processes, vols. 1, 2, Springer-Verlag, Berlin 1965.

    MATH  Google Scholar 

  5. FUKUSHIMA, M.: Dirichlet forms and Markov processes, Kodansha and North-Holland, 1980.

    MATH  Google Scholar 

  6. FUKUSHIMA, M. and M. OKADA: ‘On conformai martingale diffusions and pluripolar sets’, J. Functional Anal. 55 (1984), 377–388.

    Article  MathSciNet  MATH  Google Scholar 

  7. GAVEAU, B. and J. ŁAWRYNOWICZ: ‘Intégrale de Dirichlet sur une variété complexe I’, in: Lect. Notes in Math. 919, Springer 1982, pp. 131–167.

    Google Scholar 

  8. KALINA, J. and J. ŁAWRYNOWICZ: ‘Foliations and the generalized complex Monge-Ampère equations’, Banach Center Publications 11 (1983), 111–119.

    Google Scholar 

  9. ŁAWRYNOWICZ, J. and M. OKADA: ‘Canonical diffusion and foliation involving the complex hessian’, Bull. Polish Acad. Sei. Math. 34 (1986), 661–667.

    MATH  Google Scholar 

  10. OKADA, M.: ‘Espaces de Dirichlet généraux en analyse complexe’, J. Functional Anal. 46 (1982), 396–410.

    Article  MathSciNet  MATH  Google Scholar 

  11. OKADA, M.: ‘Sur une capacité définie par la forme de Dirichlet associée aux fonctions plurisousharmoniques’, Tôhoku Math. J. 35 (1983), 513–517.

    Article  MathSciNet  MATH  Google Scholar 

  12. RAUCH, J. and B.A. TAYLOR: ‘The Dirichlet problem for the multidimensional Monge-Ampère equation’, Rocky Mountain J. Math. 7 (1977), 345–364.

    Article  MathSciNet  MATH  Google Scholar 

  13. SICIAK, J.: ‘Extremal plurisubharmonic functions and capacities in ℂn, Lect. Notes Sophia Univ. 14 (1982).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Kluwer Academic Publishers

About this chapter

Cite this chapter

Okada, M. (1989). Symbolic Calculus Applied to Convex Functions and Associated Diffusions. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_29

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2643-1_29

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7693-7

  • Online ISBN: 978-94-009-2643-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics