Skip to main content
SpringerLink
Log in

Some Recent Applications of Bilinear Integration

  • Conference paper
Vector Measures, Integration and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 201))

Abstract

Three topics featuring bilinear integration are described: the noncommutative Feynman-Kac formula, the connection between stationary state and time-dependent scattering theory and the stochastic integration of vectorvalued processes.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
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. W.O. Amrein, V. Georgescu and J.M. Jauch, Stationary state scattering theory, Helv. Phys. Acta. 44 (1971) 407–434.

    MathSciNet  Google Scholar 

  2. R. Bartle, A general bilinear vector integral, Studia Math. 15 (1956), 337–351.

    MATH  MathSciNet  Google Scholar 

  3. I. Dobrakov, On integration in Banach spaces I, Czech. Math. J. 20 (1970), 511–536.

    MathSciNet  Google Scholar 

  4. I. Dobrakov, On integration in Banach spaces, II, Czech. Math. J. 20 (1970), 680–695.

    Google Scholar 

  5. D.J.H. Garling, Brownian motion and UMD-spaces, in: “Probability and Banach Spaces”. (Zaragoza, 1985), 36–49, Lecture Notes in Math. 1221, Springer-Verlag, Berlin, 1986.

    Chapter  Google Scholar 

  6. B. Jefferies, Evolution Processes and the Feynman-Kac Formula, Kluwer Academic Publishers, Dordrecht/Boston/London, 1996.

    Google Scholar 

  7. B. Jefferies and S. Okada, Bilinear integration in tensor products, Rocky Mountain J. Math. 28 (1998), 517–545.

    Article  MathSciNet  Google Scholar 

  8. -Dominated semigroups of operators and evolution processes, Hokkaido Math. J., 33 (2004), 127–151.

    MathSciNet  Google Scholar 

  9. I. Kluvánek, Applications of vector measures. Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979), pp. 101–134, Contemp. Math., 2, Amer. Math. Soc., Providence, R.I., 1980.

    Google Scholar 

  10. G. Köthe, Topological vector spaces Vol II, Grundlehren der mathematischen Wissenschaften 237, Springer-Verlag, Berlin, New York, 1979.

    Google Scholar 

  11. J. Rosiński and Z. Suchanecki, On the space of vector-valued functions integrable with respect to the white noise, Colloq. Math. 43 (1980), 183–201.

    MathSciNet  Google Scholar 

  12. J.M.A.M. van Neerven and L. Weis, Stochastic integration of functions with values in a Banach space, Studia Math. 166 (2005), 131–170

    Article  MATH  MathSciNet  Google Scholar 

  13. J.M.A.M. van Neerven, M.C. Veraar and L. Weis, Stochastic integration in UMD Banach spaces, Ann. Probab. 35 (2007), 1438–1478.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, UNSW NSW, 2052, Australia

    Brian Jefferies

Authors
  1. Brian Jefferies
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Facultad de Matemáticas, Universidad de Sevilla, 41080, Sevilla, Spain

    Guillermo P. Curbera

  2. Fachbereich 6: Mathematik, Universität Siegen, 57068, Siegen, Germany

    Gerd Mockenhaupt

  3. Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85072, Eichstätt, Germany

    Werner J. Ricker

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Jefferies, B. (2009). Some Recent Applications of Bilinear Integration. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_23

Download citation

Publish with us

Policies and ethics

Search

Navigation